Modules Over Affine Lie Algebras At Critical Level And Quantum Groups PDF Download
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| Author | : Qian Lin (Electrical engineer) |
| Publisher | : |
| Total Pages | : 47 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
Download Modules Over Affine Lie Algebras at Critical Level and Quantum Groups Book in PDF, ePub and Kindle
There are two algebras associated to a reductive Lie algebra g: the De Concini- Kac quantum algebra and the Kac-Moody Lie algebra. Recent results show that the principle block of De Concini -Kac quantum algebra at an odd root of unity with (some) fixed central character is equivalent to the core of a certain t-structure on the derived category of coherent sheaves on certain Springer Fiber. Meanwhile, a certain category of representation of Kac-Moody Lie algebra at critical level with (some) fixed central character is also equivalent to a core of certain t-structure on the same triangulated category. Based on several geometric results developed by Bezurkvanikov et al. these two abelian categories turn out to be equivalent. i.e. the two t-structures coincide.
| Author | : Jürgen Fuchs |
| Publisher | : Cambridge University Press |
| Total Pages | : 452 |
| Release | : 1995-03-09 |
| Genre | : Mathematics |
| ISBN | : 9780521484121 |
Download Affine Lie Algebras and Quantum Groups Book in PDF, ePub and Kindle
This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.
| Author | : Susumu Ariki |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 302 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821853171 |
Download Algebraic Groups and Quantum Groups Book in PDF, ePub and Kindle
This volume contains the proceedings of the tenth international conference on Representation Theory of Algebraic Groups and Quantum Groups, held August 2-6, 2010, at Nagoya University, Nagoya, Japan. The survey articles and original papers contained in this volume offer a comprehensive view of current developments in the field. Among others reflecting recent trends, one central theme is research on representations in the affine case. In three articles, the authors study representations of W-algebras and affine Lie algebras at the critical level, and three other articles are related to crystals in the affine case, that is, Mirkovic-Vilonen polytopes for affine type $A$ and Kerov-Kirillov-Reshetikhin type bijection for affine type $E_6$. Other contributions cover a variety of topics such as modular representation theory of finite groups of Lie type, quantum queer super Lie algebras, Khovanov's arc algebra, Hecke algebras and cyclotomic $q$-Schur algebras, $G_1T$-Verma modules for reductive algebraic groups, equivariant $K$-theory of quantum vector bundles, and the cluster algebra. This book is suitable for graduate students and researchers interested in geometric and combinatorial representation theory, and other related fields.
| Author | : Yun Gao, Naihuan Jing, Michael Lau, and Kailash C. Misra |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 314 |
| Release | : 2010 |
| Genre | : Geometry, Affine |
| ISBN | : 0821858327 |
Download Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications Book in PDF, ePub and Kindle
| Author | : Bangming Deng |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 790 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821841866 |
Download Finite Dimensional Algebras and Quantum Groups Book in PDF, ePub and Kindle
"The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.
| Author | : Yun Gao |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 314 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821845071 |
Download Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications Book in PDF, ePub and Kindle
This volume contains the proceedings of the conference on Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, which was held at the Banff International Research Station, Banff, Canada, from March 2-7, 2008. Many of the papers include new results on different aspects of quantum affine algebras, extended affine Lie algebras, and their applications in other areas of mathematics and physics. Any reader interested in learning about the recent developments in quantum affine algebras and extended affine Lie algebras will benefit from this book.
| Author | : Vladimir K. Dobrev |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 246 |
| Release | : 2019-04-01 |
| Genre | : Mathematics |
| ISBN | : 3110609711 |
Download AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras Book in PDF, ePub and Kindle
The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.
| Author | : Victor G Kac |
| Publisher | : World Scientific |
| Total Pages | : 642 |
| Release | : 1989-07-01 |
| Genre | : |
| ISBN | : 9814663174 |
Download Infinite Dimensional Lie Algebras And Groups Book in PDF, ePub and Kindle
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
| Author | : Sam Kass |
| Publisher | : Univ of California Press |
| Total Pages | : 312 |
| Release | : 1990-01-01 |
| Genre | : Science |
| ISBN | : 9780520067684 |
Download Affine Lie Algebras, Weight Multiplicities, and Branching Rules Book in PDF, ePub and Kindle
00 This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference. This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference.
| Author | : Jacob Greenstein |
| Publisher | : Springer Nature |
| Total Pages | : 453 |
| Release | : 2022-03-11 |
| Genre | : Mathematics |
| ISBN | : 3030638499 |
Download Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification Book in PDF, ePub and Kindle
This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.
