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

2011/10/25 by Geck, Meinolf
#20C08 (Primary) 20C15 (Secondary) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1110.5672

Abstract

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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