The $p$-Canonical Basis for Hecke Algebras
Representation Theory
2016-02-11 v2 Category Theory
Abstract
We describe a positive characteristic analogue of the Kazhdan-Lusztig basis of the Hecke algebra of a crystallographic Coxeter system and investigate some of its properties. Using Soergel calculus we describe an algorithm to calculate this basis. We outline some known or expected applications in modular representation theory. We conclude by giving several examples.
Keywords
Cite
@article{arxiv.1510.01556,
title = {The $p$-Canonical Basis for Hecke Algebras},
author = {Lars Thorge Jensen and Geordie Williamson},
journal= {arXiv preprint arXiv:1510.01556},
year = {2016}
}
Comments
32 pages, many TikZ pictures, best viewed in colour and pdf