Kostka functions associated to complex reflection groups

2015/09/24 by Toshiaki Shoji, Shoji, Toshiaki
Mathematics · #05E05 #20G10 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:05E05 #msc:20G10

paper · pdf · doi:10.48550/arxiv.1509.07413

21 pages

arxiv created 2015/09/24 · arxiv updated 2015/09/25

Abstract

Kostka functions K^±_{λ, μ}(t) associated to complex reflection groups are a generalization of Kostka polynomials, which are indexed by a pair λ, μ of r-partitions and a sign +, -. It is expected that there exists a close connection between those Kostka functions and the intersection cohomology associated to the enhanced variety X of level r. In this paper, we study combinatorial properties of Kostka functions by making use of the geometry of X. In particular, we show that if μ is of the form μ= (-,…, -, ξ) and λ is arbitrary, K^-_{λ, μ}(t) has a Lascoux-Schützenberger type combinatorial description.

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