Kostka functions associated to complex reflection groups and a conjecture of Finkelberg-Ionov

作     者：Toshiaki Shoji 

作者机构：Department of Mathematics Tongji University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2018年第61卷第2期

页      面：353-384页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Kostka functions complex reflection groups conjecture of Finkelberg Ionov 

摘      要：Kostka functions K_(λ,μ)~±(t), indexed by r-partitions λ and μ of n, are a generalization of Kostka polynomials K_(λ,μ)(t) indexed by partitions λ,μ of n. It is known that Kostka polynomials have an interpretation in terms of Lusztig s partition function. Finkelberg and Ionov(2016) defined alternate functions K_(λ,μ)(t) by using an analogue of Lusztig s partition function, and showed that K_(λ,μ)(t) ∈Z≥0[t] for generic μ by making use of a coherent realization. They conjectured that K_(λ,μ)(t) coincide with K_(λ,μ)^-(t). In this paper, we show that their conjecture holds. We also discuss the multi-variable version, namely, r-variable Kostka functions K_(λ,μ)~±(t_1,…,t_r).