Download or read book Representations of Algebras Geometry and Physics written by Kiyoshi Igusa and published by American Mathematical Soc.. This book was released on 2021-05-17 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25–30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Reflecting recent developments in modern representation theory of algebras, the selected topics include an introduction to a new class of quiver algebras on surfaces, called “geodesic ghor algebras”, a detailed presentation of Feynman categories from a representation-theoretic viewpoint, connections between representations of quivers and the structure theory of Coxeter groups, powerful new applications of approximable triangulated categories, new results on the heart of a t t-structure, and an introduction to methods of constructive category theory.
Download or read book Representations of Algebras Geometry and Physics written by Alex Martsinkovsky and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Noncommutative Algebraic Geometry and Representations of Quantized Algebras written by A. Rosenberg and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others.
Download or read book Geometric Representation Theory and Extended Affine Lie Algebras written by Erhard Neher and published by American Mathematical Soc.. This book was released on 2011 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.
Download or read book Lie Groups and Algebras with Applications to Physics Geometry and Mechanics written by D.H. Sattinger and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
Download or read book Representation Theory Mathematical Physics and Integrable Systems written by Anton Alekseev and published by Springer Nature. This book was released on 2022-02-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.
Download or read book Representation Theory and Complex Geometry written by Victor Ginzburg and published by Birkhauser. This book was released on 2005-05-01 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: [see attached] This second edition of {\it Representation Theory and Complex Geometry} provides an overview of significant advances in representation theory from a geometric standpoint. A geometrically-oriented treatment has long been desired, especially since the discovery of {\cal D}-modules in the early '80s and the quiver approach to quantum groups in the early '90s. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician. Thus, Chapters 1-3 and 5-6 provide some basics in symplectic geometry, Borel--Moore homology, the geometry of semisimple groups, equivariant algebraic K-theory "from scratch," and the topology and algebraic geometry of flag varieties and conjugacy classes, respectively. The material covered by Chapters 5 and 6, as well as most of Chapter 3, has never been presented in book form. Chapters 3-4 and 7-8 present a uniform approach to representation theory of three quite different objects: Weyl groups, Lie algebra sln, and the Iwahori--Hecke algebra. The results of Chapters 4 and 8, with complete proofs are not to be found elsewhere in the literature. This second edition contains substantial updates and revisions to include more standard classical results in chapters 2, 3, 5, and 6 as well as two new chapters. Chapter 9 treats the applications of {\cal D}-modules to Lie groups, and includes the study of * Differential operators on a semisimple group and on its flag manifold; * the famous Beilinson--Bernstein Localization Theorem reducing the study of {\it g}-modules to that of {\cal D} modules; * the so-called Harish--Chandra holonomic system. Chapter 10 isdevoted to some very exciting developments connecting the representations of quantum groups to the geometry of "quiver varieties," introduced by Lusztig and Nakajima. The subject is closely related to many other important topics such as the McKay correspondence, semismall resolutions and Hilbert schemes. Overall, this chapter puts the representation theory of Kac--Moody algebras and quantum groups in this broader context. The exposition is practically self-contained with each chapter potentially serving as a basis for a graduate course or seminar. An excellent glossary of notation, comprehensive bibliography and extensive index round out this new edition. The techniques developed here play an essential role in the development of the Langlands program and can be successfully applied to representation theory, quantum groups and quantum field theory, affine Lie algebras, algebraic geometry, and mathematical physics.
Download or read book Elliptic Quantum Groups written by Hitoshi Konno and published by Springer Nature. This book was released on 2020-09-14 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation. Based on research by the author and his collaborators, the book presents a comprehensive survey on the subject including a brief history of formulations and applications, a detailed formulation of the elliptic quantum group in the Drinfeld realization, explicit construction of both finite and infinite-dimensional representations, and a construction of the vertex operators as intertwining operators of these representations. The vertex operators are important objects in representation theory of quantum groups. In this book, they are used to derive the elliptic q-KZ equations and their elliptic hypergeometric integral solutions. In particular, the so-called elliptic weight functions appear in such solutions. The author’s recent study showed that these elliptic weight functions are identified with Okounkov’s elliptic stable envelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkov’s geometric approach to quantum integrable systems is a rapidly growing topic in mathematical physics related to the Bethe ansatz, the Alday-Gaiotto-Tachikawa correspondence between 4D SUSY gauge theories and the CFT’s, and the Nekrasov-Shatashvili correspondences between quantum integrable systems and quantum cohomology. To invite the reader to such topics is one of the aims of this book.
Download or read book Clifford Algebras written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.
Download or read book Noncommutative Algebraic Geometry and Representations of Quantized Algebras written by A. Rosenberg and published by . This book was released on 2014-01-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Group Representations written by William Mark Goldman and published by American Mathematical Soc.. This book was released on 1988 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains papers based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987. This work offers an understanding of the state of research in the geometry of group representations and their applications.
Download or read book Lie Groups Geometry and Representation Theory written by Victor G. Kac and published by Springer. This book was released on 2018-12-12 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)
Download or read book Branes and DAHA Representations written by Sergei Gukov and published by Springer. This book was released on 2023-08-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which comes from string theory, is explored in the book. This book provides a detailed description of the geometric approach to the representation theory of the double affine Hecke algebra (DAHA) of rank one. Spherical DAHA is known to arise from the deformation quantization of the moduli space of SL(2,C) flat connections on the punctured torus. The authors demonstrate the study of the topological A-model on this moduli space and establish a correspondence between Lagrangian branes of the A-model and DAHA modules. The finite-dimensional DAHA representations are shown to be in one-to-one correspondence with the compact Lagrangian branes. Along the way, the authors discover new finite-dimensional indecomposable representations. They proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action are identified. The relationship of Coulomb branch geometry and algebras of line operators in 4d N = 2* theories to the double affine Hecke algebra is studied further by using a further connection to the fivebrane system for the class S construction. The book is targeted at experts in mathematical physics, representation theory, algebraic geometry, and string theory. This is an open access book.
Download or read book Homotopy Theory Via Algebraic Geometry and Group Representations written by Mark E. Mahowald and published by American Mathematical Soc.. This book was released on 1998-01-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.
Download or read book Recent Advances in Representation Theory Quantum Groups Algebraic Geometry and Related Topics written by Pramod M. Achar and published by American Mathematical Society. This book was released on 2014-08-27 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.
Download or read book Quantum Algebras and Poisson Geometry in Mathematical Physics written by Mikhail Vladimirovich Karasev and published by American Mathematical Soc.. This book was released on 2005 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents applications of Poisson geometry to some fundamental well-known problems in mathematical physics. This volume is suitable for graduate students and researchers interested in mathematical physics. It uses methods such as: unexpected algebras with non-Lie commutation relations, dynamical systems theory, and semiclassical asymptotics.
Download or read book Representation Theory of Algebraic Groups and Quantum Groups written by Akihiko Gyoja and published by . This book was released on 2011-03-30 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
