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arXiv · 2311.07904

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

Aritra Bhattacharya·T V Ratheesh·Sankaran Viswanath
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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 $\widehat{\mathfrak{sl}_n}$. Finally, we indicate how our main results generalize to the modified Hall-Littlewood case.

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Aritra Bhattacharya, T V Ratheesh, Sankaran Viswanath. 2023-11-14. Monomial expansions for $q$-Whittaker and modified Hall-Littlewood polynomials. https://arxiv.org/abs/2311.07904

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