Hecke algebras and involutions in Weyl groups

By G. Lusztig, D. Vogan. 2011

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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.

Subfields: Geometry and Topology, Mathematical Physics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/c364f032f3e2c038d2283756daf20b0e45c96ae2