2015/01/24 by Liu Shiyuan, Shiyuan, Liu, Toshiaki Shoji +1 · 1 citation
Mathematics · #05E05 #05E10 #20G10 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:05E05 #msc:05E10 #msc:20G10
paper · pdf · doi:10.48550/arxiv.1501.05996
33 pages, including tables of double Kostka polynomials
arxiv created 2015/01/24 · openalex publication_date 2015/01/24 · arxiv updated 2015/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Double Kostka polynomials are polynomials indexed by a pair of double partitions. As in the ordinary case, double Kostka polynomials are defined in terms of Schur functions and Hall-Littlewood functions associated to double partitions. In this paper, we study combinatorial properties of those double Kostka polynomials and Hall-Littlewood functions. In particular, we show that the Lascoux-Schutzenberger type formula holds for double Kostka polynomials in certain cases. Moreover, we show that the Hall bimodule introduced by Finkelberg-Ginzburg-Travkin is isomorphic to the ring of symmetric functions with two types of variables, which gives an alternate approach for their result.