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 Geometric Group Theory written by Clara Löh and published by Springer. This book was released on 2017-12-19 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
Download or read book Representation Theory and Complex Geometry written by Neil Chriss and published by . This book was released on 1997 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an attempt to provide an overview of some of the recent advances in representation theory from a geometric standpoint. A geometrically-oriented treatment is very timely and has long been desired, especially since the discovery of D-modules in the early '80s and the quiver approach to quantum groups in the early '90s.
Download or read book Poisson Geometry Deformation Quantisation and Group Representations written by Simone Gutt and published by Cambridge University Press. This book was released on 2005-06-21 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to Poisson geometry suitable for graduate students.
Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg and published by Springer Science & Business Media. This book was released on 2011-10-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Download or read book D Modules Perverse Sheaves and Representation Theory written by Ryoshi Hotta and published by Springer Science & Business Media. This book was released on 2007-11-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
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 Frobenius Splitting Methods in Geometry and Representation Theory written by Michel Brion and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically develops the theory of Frobenius splittings and covers all its major developments. Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings—definitions, properties and examples—to cutting edge research.
Download or read book Groups written by R. P. Burn and published by Cambridge University Press. This book was released on 1987-09-03 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.
Download or read book Structure and Geometry of Lie Groups written by Joachim Hilgert and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.
Download or read book Representations of Algebraic Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 2003 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Download or read book Lectures on Representations of Surface Groups written by François Labourie and published by . This book was released on 2013 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of these notes is the character variety of representations of a surface group in a Lie group. The author emphasizes the various points of view (combinatorial, differential, and algebraic) and is interested in the description of its smooth points, symplectic structure, volume and connected components. He also shows how a three manifold bounded by the surface leaves a trace in this character variety. These notes were originally designed for students with only elementary knowledge of differential geometry and topology. In the first chapters, the author does not focus on the details of the differential geometric constructions and refers to classical textbooks, while in the more advanced chapters proofs occasionally are provided only for special cases where they convey the flavor of the general arguments. These notes might also be used by researchers entering this fast expanding field as motivation for further studies. The concluding paragraph of every chapter provides suggestions for further research.
Download or read book A Journey Through Representation Theory written by Caroline Gruson and published by Springer. This book was released on 2018-10-23 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.
Download or read book Geometry of Defining Relations in Groups written by A.Yu. Ol'shanskii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Ht moi - ..., si favait su comment en reveniT, One service mathematics hal rendered the je n'y serais point aile.' human race. It has put C.
Download or read book The Geometry of Heisenberg Groups written by Ernst Binz and published by American Mathematical Soc.. This book was released on 2008 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.
Download or read book The Geometry and Topology of Coxeter Groups written by Michael Davis and published by Princeton University Press. This book was released on 2008 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.
