Hecke algebras and involutions in Weyl groups

Details Hecke algebras and involutions in Weyl groups Hecke algebras and involutions in Weyl groups

2011-09-21

arxiv.org/abs/1109.4606v3

Mathematics

Representation Theory

25 pages

Scientific paper

For any two involutions y,w in a Weyl group (y\le w), let P_{y,w} be the polynomial defined in [KL]. In this paper we define a new polynomial P^\sigma_{y,w} whose i-th coefficient is a_i-b_i where the i-th coefficient of P_{y,w} is a_i+b_i (a_i,b_i are natural numbers). These new polynomials are of interest for the theory of unitary representations of complex reductive groups. We present an algorithm for computing these polynomials.

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