Kazhdan--Lusztig cells and the Frobenius--Schur indicator

Details Kazhdan--Lusztig cells and the Frobenius--Schur indicator Kazhdan--Lusztig cells and the Frobenius--Schur indicator

2011-10-25

arxiv.org/abs/1110.5672v2

Mathematics

Representation Theory

12 pages; the new version contains some additions in Section 3

Scientific paper

Let $W$ be a finite Coxeter group. It is well-known that the number of involutions in $W$ is equal to the sum of the degrees of the irreducible characters of $W$. Following a suggestion of Lusztig, we show that this equality is compatible with the decomposition of $W$ into Kazhdan--Lusztig cells. The proof uses a generalisation of the Frobenius--Schur indicator to symmetric algebras, which may be of independent interest.

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