Coxeter groups, Hecke algebras and their representations

1986 ◽  
pp. 1-31
Author(s):  
Jian-Yi Shi
Keyword(s):  
Coxeter Groups ◽  
Hecke Algebras

scholarly journals Hecke algebras and involutions in Coxeter groups

2015 ◽  
pp. 365-398
Author(s):  
George Lusztig ◽  
David A. Vogan
Keyword(s):  
Coxeter Groups ◽  
Hecke Algebras

scholarly journals Automorphisms of Coxeter Groups and Lusztig’s Conjectures for Hecke Algebras with Unequal Parameters

2009 ◽  
Vol 195 ◽  
pp. 153-164
Author(s):  
Cédric Bonnafé
Keyword(s):  
Weight Function ◽  
Solvable Group ◽  
Coxeter Groups ◽  
Hecke Algebras ◽  
Finite Solvable Group ◽  
Coxeter System ◽  
Group Of Automorphisms

AbstractLet (W,S) be a Coxeter system, let G be a finite solvable group of automorphisms of (W, S) and let ϕ be a weight function which is invariant under G. Let ϕG denote the weight function on WG obtained by restriction from ϕ. The aim of this paper is to compare the a-function, the set of Duflo involutions and the Kazhdan-Lusztig cells associated with (W, ϕ) and to (WG,ϕG), provided that Lusztig’s Conjectures hold.

scholarly journals Automorphisms of Generic Iwahori–Hecke Algebras and Integral Group Rings of Finite Coxeter Groups

1997 ◽  
Vol 197 (2) ◽  
pp. 615-655 ◽  
Author(s):  
Frauke M Bleher ◽  
Meinolf Geck ◽  
Wolfgang Kimmerle
Keyword(s):  
Coxeter Groups ◽  
Hecke Algebras ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings

Representations of Coxeter groups and Hecke algebras

1979 ◽  
Vol 53 (2) ◽  
pp. 165-184 ◽  
Author(s):  
David Kazhdan ◽  
George Lusztig
Keyword(s):  
Coxeter Groups ◽  
Hecke Algebras

scholarly journals ON CANONICAL BASES AND INDUCTION OF -GRAPHS

2018 ◽  
Vol 239 ◽  
pp. 1-41
Author(s):  
JOHANNES HAHN
Keyword(s):  
Coxeter Groups ◽  
Canonical Basis ◽  
Hecke Algebras ◽  
Free Module ◽  
Base Change ◽  
Manuscripta Math ◽  
Laurent Polynomials ◽  
Graph Algebras ◽  
Canonical Bases ◽  
Change Matrix

A canonical basis in the sense of Lusztig is a basis of a free module over a ring of Laurent polynomials that is invariant under a certain semilinear involution and is obtained from a fixed “standard basis” through a triangular base change matrix with polynomial entries whose constant terms equal the identity matrix. Among the better known examples of canonical bases are the Kazhdan–Lusztig basis of Iwahori–Hecke algebras (see Kazhdan and Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165–184), Lusztig’s canonical basis of quantum groups (see Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3(2) (1990), 447–498) and the Howlett–Yin basis of induced $W$-graph modules (see Howlett and Yin, Inducing W-graphs I, Math. Z. 244(2) (2003), 415–431; Inducing W-graphs II, Manuscripta Math. 115(4) (2004), 495–511). This paper has two major theoretical goals: first to show that having bases is superfluous in the sense that canonicalization can be generalized to nonfree modules. This construction is functorial in the appropriate sense. The second goal is to show that Howlett–Yin induction of $W$-graphs is well-behaved a functor between module categories of $W$-graph algebras that satisfies various properties one hopes for when a functor is called “induction,” for example transitivity and a Mackey theorem.

On the Left Cell Representations of Iwahori-Hecke Algebras of Finite Coxeter Groups

1996 ◽  
Vol 54 (3) ◽  
pp. 475-488 ◽  
Author(s):  
Andrew Mathas
Keyword(s):  
Coxeter Groups ◽  
Hecke Algebras ◽  
Left Cell

Coxeter groups and Hecke algebras

2008 ◽  
pp. 183-228
Author(s):  
Bangming Deng ◽  
Jie Du ◽  
Brian Parshall ◽  
Jianpan Wang
Keyword(s):  
Coxeter Groups ◽  
Hecke Algebras

‘Good’ Elements of Finite Coxeter Groups and Representations of Iwahori-Hecke Algebras

1997 ◽  
Vol 74 (2) ◽  
pp. 275-305 ◽  
Author(s):  
M Geck ◽  
J Michel
Keyword(s):  
Coxeter Groups ◽  
Hecke Algebras

scholarly journals Some applications of CHEVIE to the theory of algebraic groups

2011 ◽  
Vol 27 (1) ◽  
pp. 64-94
Author(s):  
MEINOLF GECK ◽  
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Coxeter Groups ◽  
Algebraic Groups ◽  
Hecke Algebras ◽  
Lie Theory ◽  
Combinatorial Structures ◽  
Springer Correspondence

The computer algebra system CHEVIE is designed to facilitate computations with various combinatorial structures arising in Lie theory, like finite Coxeter groups and Hecke algebras. We discuss some recent examples where CHEVIE has been helpful in the theory of algebraic groups, in questions related to unipotent classes, the Springer correspondence and Lusztig families.

Sign in / Sign up

Export Citation Format

Share Document