Algebraic Combinatorics And Quantum Groups PDF Download
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Author | : Naihuan Jing |
Publisher | : World Scientific |
Total Pages | : 171 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9812384464 |
Download Algebraic Combinatorics and Quantum Groups Book in PDF, ePub and Kindle
Algebraic combinatorics has evolved into one of the most active areas of mathematics during the last several decades. Its recent developments have become more interactive with not only its traditional field representation theory but also algebraic geometry, harmonic analysis and mathematical physics.This book presents articles from some of the key contributors in the area. It covers Hecke algebras, Hall algebras, the Macdonald polynomial and its deviations, and their relations with other fields.
Author | : Susumu Ariki |
Publisher | : American Mathematical Soc. |
Total Pages | : 169 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821832328 |
Download Representations of Quantum Algebras and Combinatorics of Young Tableaux Book in PDF, ePub and Kindle
This book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the study of representations of quantum groups. Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and toapply the theory to representations of Hecke algebras. The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type $A {r-1 {(1) $ as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be thecombinatorics of Young tableaux. The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type. The book is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups and quantum groups, the theory of Hecke algebras, algebraic combinatorics, andrelated fields.
Author | : Anatoli Klimyk |
Publisher | : Springer Science & Business Media |
Total Pages | : 568 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3642608965 |
Download Quantum Groups and Their Representations Book in PDF, ePub and Kindle
This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Author | : Thomas Timmermann |
Publisher | : European Mathematical Society |
Total Pages | : 436 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9783037190432 |
Download An Invitation to Quantum Groups and Duality Book in PDF, ePub and Kindle
This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of $C^*$-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, $C^*$-algebras, and von Neumann algebras.
Author | : Benjamin Enriquez |
Publisher | : European Mathematical Society |
Total Pages | : 148 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9783037190470 |
Download Quantum Groups Book in PDF, ePub and Kindle
The volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius-Perron dimensions, and the classification of tensor categories. The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups. The preface puts the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics.
Author | : Daniel Krob |
Publisher | : Springer Science & Business Media |
Total Pages | : 815 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662041669 |
Download Formal Power Series and Algebraic Combinatorics Book in PDF, ePub and Kindle
This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...
Author | : Leonid I. Korogodski |
Publisher | : American Mathematical Soc. |
Total Pages | : 162 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 0821803360 |
Download Algebras of Functions on Quantum Groups: Part I Book in PDF, ePub and Kindle
The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.
Author | : Matilde Marcolli |
Publisher | : Springer Science & Business Media |
Total Pages | : 247 |
Release | : 2010-11-02 |
Genre | : Mathematics |
ISBN | : 3834898317 |
Download Quantum Groups and Noncommutative Spaces Book in PDF, ePub and Kindle
This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.
Author | : Ken Brown |
Publisher | : Birkhäuser |
Total Pages | : 339 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 303488205X |
Download Lectures on Algebraic Quantum Groups Book in PDF, ePub and Kindle
This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.
Author | : Georgia Benkart |
Publisher | : American Mathematical Soc. |
Total Pages | : 270 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821839241 |
Download Representations of Algebraic Groups, Quantum Groups, and Lie Algebras Book in PDF, ePub and Kindle
Covers various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. This book outlines connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic.