Abstract
Kostka functions K , ± (t), indexed by r-partitions λ and ÎŒ of n, are a generalization of Kostka polynomials Kλ,ÎŒ(t) indexed by partitions λ,ÎŒ of n. It is known that Kostka polynomials have an interpretation in terms of Lusztigâs partition function. Finkelberg and Ionov (2016) defined alternate functions Kλ,ÎŒ(t) by using an analogue of Lusztigâs partition function, and showed that Kλ,ÎŒ(t) â Z>0[t] for generic ÎŒ by making use of a coherent realization. They conjectured that Kλ,ÎŒ(t) coincide with K , - (t). In this paper, we show that their conjecture holds. We also discuss the multi-variable version, namely, r-variable Kostka functions K , ± (t1,..., t r ).
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