A skein-like multiplication algorithm for unipotent Hecke algebras Journal Article uri icon

Overview

abstract

  • Let ; ; ; G; G; ; ; be a finite group of Lie type (e.g. ; ; ; ; G; ; L; n; ; (; ; ; F; ; q; ; ); ; GL_n(mathbb {F}_q); ; ; ) and ; ; ; U; U; ; ; a maximal unipotent subgroup of ; ; ; G; G; ; ; . If ; ; ; ψ; psi; ; ; is a linear character of ; ; ; U; U; ; ; , then the unipotent Hecke algebra is ; ; ; ; ; ; H; ; ψ; ; =; ; ; E; n; d; ; ; ; C; ; G; ; ; (; ; ; I; n; d; ; U; G; ; (; ψ; ); ); ; mathcal {H}_psi =mathrm {End}_{mathbb {C}G} (mathrm {Ind}_U^G(psi )); ; ; . Unipotent Hecke algebras have a natural basis coming from double cosets of ; ; ; U; U; ; ; in ; ; ; G; G; ; ; . This paper describes relations for reducing products of basis elements, and gives a detailed description of the implications in the case ; ; ; ; G; =; G; ; L; n; ; (; ; ; F; ; q; ; ); ; G=GL_n(mathbb {F}_q); ; ; .

publication date

  • January 1, 2007

Date in CU Experts

  • September 20, 2013 11:07 AM

Full Author List

  • Thiem N

author count

  • 1

Other Profiles

International Standard Serial Number (ISSN)

  • 0002-9947

Electronic International Standard Serial Number (EISSN)

  • 1088-6850

Additional Document Info

start page

  • 1685

end page

  • 1724

volume

  • 359

issue

  • 4