Representations of Quantum Algebras and Combinatorics of Young Tableaux is popular PDF and ePub book, written by Susumu Ariki in 2002, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Representations of Quantum Algebras and Combinatorics of Young Tableaux can be Read Online from any device for your convenience.
Representations of Quantum Algebras and Combinatorics of Young Tableaux Book PDF Summary
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.
Detail Book of Representations of Quantum Algebras and Combinatorics of Young Tableaux PDF
- Author : Susumu Ariki
- Release : 21 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821832325
- Genre : Mathematics
- Total Page : 169 pages
- Language : English
- PDF File Size : 19,7 Mb
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