Algebraic Combinatorics and Quantum Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Combinatorics and Quantum Groups write by Naihuan Jing. This book was released on 2003. Algebraic Combinatorics and Quantum Groups available in PDF, EPUB and Kindle. Algebraic combinatorics has evolved into one of the most active areas of mathematics. Its developments have become more interactive with not only its traditional field representation theory but also geometry, mathematical physics and harmonic analysis. 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.
Algebraic Combinatorics and Quantum Groups
Algebraic Combinatorics and Quantum Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Combinatorics and Quantum Groups write by Naihuan Jing. This book was released on 2003. Algebraic Combinatorics and Quantum Groups available 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.
Representations of Quantum Algebras and Combinatorics of Young Tableaux
Representations of Quantum Algebras and Combinatorics of Young Tableaux - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representations of Quantum Algebras and Combinatorics of Young Tableaux write by Susumu Ariki. This book was released on 2002. Representations of Quantum Algebras and Combinatorics of Young Tableaux available 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.
An Invitation to Quantum Groups and Duality
An Invitation to Quantum Groups and Duality - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Quantum Groups and Duality write by Thomas Timmermann. This book was released on 2008. An Invitation to Quantum Groups and Duality available 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.
Representations of Algebraic Groups, Quantum Groups, and Lie Algebras
Representations of Algebraic Groups, Quantum Groups, and Lie Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representations of Algebraic Groups, Quantum Groups, and Lie Algebras write by Georgia Benkart. This book was released on 2006. Representations of Algebraic Groups, Quantum Groups, and Lie Algebras available 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.
