Kazhdan--Lusztig cells and the Frobenius--Schur indicator
Representation Theory
2011-12-20 v2
Abstract
Let be a finite Coxeter group. It is well-known that the number of involutions in is equal to the sum of the degrees of the irreducible characters of . Following a suggestion of Lusztig, we show that this equality is compatible with the decomposition of into Kazhdan--Lusztig cells. The proof uses a generalisation of the Frobenius--Schur indicator to symmetric algebras, which may be of independent interest.
Keywords
Cite
@article{arxiv.1110.5672,
title = {Kazhdan--Lusztig cells and the Frobenius--Schur indicator},
author = {Meinolf Geck},
journal= {arXiv preprint arXiv:1110.5672},
year = {2011}
}
Comments
12 pages; the new version contains some additions in Section 3