Action of longest element on a Hecke algebra cell module

George Lusztig

Vol. 279 (2015), No. 1-2, 383–396

DOI: 10.2140/pjm.2015.279.383

Abstract

By a result of Mathas, the basis element $T_{w_0}$ of the Hecke algebra of a finite Coxeter group acts in the canonical basis of a cell module as a permutation matrix times plus or minus a power of $v$. We generalize this result to the unequal parameter case. We also show that the image of $T_{w_0}$ in the corresponding asymptotic Hecke algebra is given by a simple formula.

Keywords

Hecke algebra, left cell, Weyl group

Mathematical Subject Classification 2010

Primary: 20F55, 20G15

Milestones

Received: 3 March 2015

Accepted: 28 June 2015

Published: 21 December 2015