Monomial expansions for q-Whittaker and modified Hall-Littlewood polynomials

2023/11/14 by Aritra Bhattacharya, Bhattacharya, Aritra, T V Ratheesh +3
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2311.07904

Abstract

We consider the monomial expansion of the q-Whittaker polynomials given by the fermionic formula and via the inv and quinv statistics. We construct bijections between the parametrizing sets of these three models which preserve the x- and q-weights, and which are compatible with natural projection and branching maps. We apply this to the limit construction of local Weyl modules and obtain a new character formula for the basic representation of \widehat\mathfraksl_n. Finally, we indicate how our main results generalize to the modified Hall-Littlewood case.

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