Gyojas $W$-Graph-Algebra und zellul\"are Struktur von Iwahori-Hecke-Algebren

TL;DR

This paper provides an overview of Coxeter groups, Iwahori-Hecke algebras, Lusztig's asymptotic algebras, cellular algebras, and introduces Gyoja's W-graph algebra along with the W-graph decomposition conjecture.

Contribution

It introduces Gyoja's W-graph algebra and discusses the cellular structure of Iwahori-Hecke algebras, connecting various algebraic concepts and conjectures.

Findings

Discussion of cellularity of Iwahori-Hecke algebras

Introduction to Gyoja's W-graph algebra

Overview of the W-graph decomposition conjecture

Abstract

On overview of Coxeter groups $W$, their Iwahori-Hecke algebras $H$, Lusztig's asymptotic algebras $J$, cellular algebras in general and cellularity of $H$ in particular, as well as an introduction to Gyoja's $W$-graph algebra and the $W$-graph decomposition conjecture.