Hecke algebras and involutions in Weyl groups

2011/09/21 by George Lusztig, Lusztig, George, David A. Vogan +2 · 3 citations
Chemistry · Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Molecular spectroscopy and chirality #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1109.4606

25 pages

openalex publication_date 2011/09/21 · arxiv created 2011/11/04 · arxiv updated 2011/11/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For any two involutions y,w in a Weyl group (y≤ w), let P_y,w be the polynomial defined in [KL]. In this paper we define a new polynomial P^σ_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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