Download or read book Structure of the Standard Modules for the Affine Lie Algebra A 1 1 written by James Lepowsky and published by American Mathematical Soc.. This book was released on 1985 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The affine Kac-Moody algebra $A_1 DEGREES{(1)}$ has served as a source of ideas in the representation theory of infinite-dimensional affine Lie algebras. This book develops the calculus of vertex operators to solve the problem of constructing all the standard $A_1 DEGREES{(1)}$-modules in the homogeneou
Download or read book Structure of the Standard Modules for the Affine Lie Algebra A 1 1 written by James Lepowsky and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structures of the Level One Standard Modules for the Affine Lie Algebras B l 1 F 4 1 and G 2 1 written by Marly Mandia and published by American Mathematical Soc.. This book was released on 1987 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lie Algebras and Related Topics written by Daniel J. Britten and published by American Mathematical Soc.. This book was released on 1986 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.
Download or read book Mathematical Aspects Of String Theory Proceedings Of The Conference On Mathematical Aspects Of String Theory written by Shing-tung Yau and published by World Scientific. This book was released on 1987-09-01 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:Introduction to Quantum Field Theory, Path Integrals and String (B Hatfield)From Polyakov to Moduli (J Polchinski)Geometry of Quantum Strings (E D'Hoker & D H Phong)BRST Quantization and BRST Cohomology (N Marcus & A Sagnotti)Analytic Structure of Two-Dimensional Quantum Field Theories (P Nelson)Geometrical Meaning of Currents in String Theory (O Alvarez & P Windey)String Field Theory and the Geometry of Moduli Space (S Giddings)String Theory Without a Background Spacetime Geometry (G Horowitz)Holomorphic Curves on Manifolds of SU(3) Holonomy (E Witten)Vertex Operator Calculus (I Frenkel et al.)On Determinant Line Bundles (D Freed)h-Invariant and the Index (I Singer)Action Principles and Global Geometry (G Zuckerman)Introduction to Moduli Space of Curves (J Harris)Moduli Space of Punctured Surfaces (R Penner)Geometric Complex Coordinates for Teichmüller Space (A Marden)Asymptotics of the Selberg Zeta Function and the Polyakov Bosonic Integrand (S Wolpert)Super Riemann Surfaces (J Rabin)Divisors on Mg and the Cosmological Constant (M Chang & Z Ran)Severi Problem: A Post-Mortem (?) (Z Ran)Slope of Subvarieties of M15 (6 2/3 ≤ S15 ≤ 6 3/4) (M Chang & Z Ran)Arithmetic Intersections (G Faltings)Deformation Theory for Cohomology of Analytic Vector Bundles on Kähler Manifolds (M Green & R Lazarsfeld)Topology and Geometry in Superstring-Inspired Phenomenology (B Greene et al.)Yukawa Couplings between (2, 1)-Forms (P Candelas)Three-Dimensional Algebraic Maniforlds with C1=0 and x=-6 (G Tian & S T Yau)Hermitian-Yang-Mills Connection on Non-Kähler Manifolds (J Li & S T Yau)Existence of Kähler-Einstein Metrics on Complete Kähler Manifolds (G Tian & S T Yau)Smoothness of the Universal Deformation Space of Compact Calabi-Yau Manifolds and its Peterson-Weil Metric (G Tian)Critical Phenomena (S Shenker) Readership: Mathematical and high energy physicists. Keywords:String Theory;Proceedings;Conference;San Diego/California
Download or read book Lie Algebras of Finite and Affine Type written by Roger William Carter and published by Cambridge University Press. This book was released on 2005-10-27 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Download or read book Introduction to Vertex Operator Algebras and Their Representations written by James Lepowsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
Download or read book Lie Algebras and Related Topics written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
Download or read book Affine Vertex and W algebras written by Dražen Adamović and published by Springer Nature. This book was released on 2019-11-28 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac–Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.
Download or read book Infinite Dimensional Lie Algebras And Groups written by Victor G Kac and published by World Scientific. This book was released on 1989-07-01 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:Integrable Representation of Kac-Moody Algebras: Results and Open Problems (V Chari & A Pressley)Existence of Certain Components in the Tensor Product of Two Integrable Highest Weight Modules for Kac-Moody Algebras (SKumar)Frobenius Action on the B-Cohomology (O Mathieu)Certain Rank Two Subsystems of Kac-Moody Root Systems (J Morita)Lie Groups Associated to Kac-Moody Lie Algebras: An Analytic Approach (E Rodriguez-Carrington)Almost Split-K-Forms of Kac-Moody Algebras (G Rousseau)Global Representations of the Diffeomorphism Groups of the Circle (F Bien)Path Space Realization of the Basic Representation of An(1) (E Date et al)Boson-Fermion Correspondence Over (C De Concini et al)Classification of Modular Invariant Representations of Affine Algebras (V G Kac & M Wakimoto)Standard Monomial Theory for SL2 (V Lakshmibai & C S Seshadri)Some Results on Modular Invariant Representations (S Lu)Current Algebras in 3+1 Space-Time Dimensions (J Mickelson)Standard Representations of An(1) (M Primc)Representations of the Algebra Uq(sI(2)), q-Orthogonal Polynomials and Invariants of Links (A N Kirillov & N Yu Reshetikhin)Infinite Super Grassmannians and Super Plücker Equations (M J Bergvelt)Drinfeld-Sokolov Hierarchies and t-Functions (H J Imbens)Super Boson-Fermion Correspondence of Type B (V G Kac & J W van de Leur)Prym Varieties and Soliton Equations (T Shiota)Polynomial Solutions of the BKP Hierarchy and Projective Representations of Symmetric Groups (Y You)Toward Generalized Macdonald's Identities (D Bernard)Conformal Theories with Non-Linearly Extended Virasoro Symmetries and Lie Algebra Classification (A Bilal & J-LGervais)Extended Conformal Algebras from Kac-Moody Algebras (P Bouwknegt)Meromorphic Conformal Field Theory (P Goddard)Local Extensions of the U(1) Current Algebra and Their Positive Energy Representations (R R Paunov & I T Todorov)Conformal Field Theory on Moduli Family of Stable Curves with Gauge Symmetries (A Tsuchiya & Y Yamada) Readership: Mathematicians and mathematical physicists
Download or read book The Mathematical Heritage of Hermann Weyl written by Raymond O'Neil Wells and published by American Mathematical Soc.. This book was released on 1988 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hermann Weyl was one of the most influential mathematicians of the twentieth century. Viewing mathematics as an organic whole rather than a collection of separate subjects, Weyl made profound contributions to a wide range of areas, including analysis, geometry, number theory, Lie groups, and mathematical physics, as well as the philosophy of science and of mathematics. The topics he chose to study, the lines of thought he initiated, and his general perspective on mathematics have proved remarkably fruitful and have formed the basis for some of the best of modern mathematical research. This volume contains the proceedings of the AMS Symposium on the Mathematical Heritage of Hermann Weyl, held in May 1987 at Duke University. In addition to honoring Weyl's great accomplishments in mathematics, the symposium also sought to stimulate the younger generation of mathematicians by highlighting the cohesive nature of modern mathematics as seen from Weyl's ideas. The symposium assembled a brilliant array of speakers and covered a wide range of topics. All of the papers are expository and will appeal to a broad audience of mathematicians, theoretical physicists, and other scientists.
Download or read book Lie Algebras Vertex Operator Algebras and Their Applications written by Yi-Zhi Huang and published by American Mathematical Soc.. This book was released on 2007 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book are based on talks given at the international conference 'Lie algebras, vertex operator algebras and their applications'. The focus of the papers is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.
Download or read book Lie Algebras and Related Topics written by D. Winter and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinite Dimensional Lie Algebras written by Victor G. Kac and published by Cambridge University Press. This book was released on 1990 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third, substantially revised edition of a monograph concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie albegras, and their representations, based on courses given over a number of years at MIT and in Paris.
Download or read book Vertex Operator Algebras and the Monster written by Igor Frenkel and published by Academic Press. This book was released on 1989-05-01 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
Download or read book Annihilating Fields of Standard Modules of mathfrak sl 2 mathbb C sim and Combinatorial Identities written by Arne Meurman and published by American Mathematical Soc.. This book was released on 1999 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde{\frak g}$, they construct the corresponding level $k$ vertex operator algebra and show that level $k$ highest weight $\tilde{\frak g}$-modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level $k$ standard modules and study the corresponding loop $\tilde{\frak g}$-module--the set of relations that defines standard modules. In the case when $\tilde{\frak g}$ is of type $A{(1)} 1$, they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of Rogers-Ramanujan type combinatorial identities.
Download or read book Generalized Vertex Algebras and Relative Vertex Operators written by Chongying Dong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.
