Topic
Longest element of a Coxeter group
About: Longest element of a Coxeter group is a research topic. Over the lifetime, 731 publications have been published within this topic receiving 18815 citations.
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Book•
29 Jun 1990TL;DR: In this article, a classification of finite and affine reflection groups is presented, including Coxeter groups, Hecke algebras and Kazhdan-Lusztig polynomials.
Abstract: Part I. Finite and Affine Reflection Groups: 1. Finite reflection groups 2. Classification of finite reflection groups 3. Polynomial invariants of finite reflection groups 4. Affine reflection groups Part II. General Theory of Coxeter Groups: 5. Coxeter groups 6. Special case 7. Hecke algebras and Kazhdan-Lusztig polynomials 8. Complements Bibliography.
2,289 citations
Book•
19 Oct 2010
TL;DR: In this paper, the basics of Bruhat order, weak order and reduced words are discussed. But they do not mention the R-polynomials of Kazhdan-Lusztig representations.
Abstract: I.- The basics.- Bruhat order.- Weak order and reduced words.- Roots, games, and automata.- II.- Kazhdan-Lusztig and R-polynomials.- Kazhdan-Lusztig representations.- Enumeration.- Combinatorial Descriptions.
1,658 citations
Book•
12 Oct 2000
TL;DR: In this article, Carartan Matrices and Finite CoXeters of Cartan MATRICES and FINITE COXETER GROUPS were involved in the construction of the BRAID MONOID and Good ELEMENTS.
Abstract: 1 CARTAN MATRICES AND FINITE COXETER GROUPS 2 PARABOLIC SUBGROUPS 3 CONJUGACY CLASSES AND SPECIAL ELEMENTS 4 THE BRAID MONOID AND GOOD ELEMENTS 5 IRREDUCIBLE CHARACTERS OF FINITE COXETER GROUPS 6 PARABOLIC SUBGROUPS AND INDUCED CHARACTERS 7 REPRESENTATION THEORY OF SYMMETRIC ALGEBRAS 8 IWAHORI-HECKE ALGEBRAS 9 CHARACTERS OF IWAHORI-HECKE ALGEBRAS 10 CHARACTER VALUES IN CLASSICAL TYPES 11 COMPUTING CHARACTER VALUES AND GENERIC DEGREES APPENDIX: TABLES FOR THE EXCEPTIONAL TYPES REFERENCES
694 citations
Book•
01 Jan 2008
TL;DR: The authors introduced the theory of Coxeter groups in the context of the Lectures on Modern Mathematics Series at the Mathematical Sciences Center in Tsinghua University on May 10, 2013.
Abstract: These notes are intended as an introduction to the theory of Coxeter groups. They closely follow my talk in the Lectures on Modern Mathematics Series at the Mathematical Sciences Center in Tsinghua University on May 10, 2013. They were prepared from the beamer presentation which I used during my talk. AMS classification numbers. Primary: 20F55, 20F65
573 citations
TL;DR: Using the theory of symmetric functions, a formula is found for r(w) when W is the symmetric group Sn and for the element w0 ∈ Sn of longest length and certain other w ∉ Sn the formula is particularly simple.
415 citations