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arXiv · 2204.06166

Representation theoretic interpretation and interpolation properties of inhomogeneous spin $q$-Whittaker polynomials

Sergei Korotkikh
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Abstract

We establish new properties of inhomogeneous spin $q$-Whittaker polynomials, which are symmetric polynomials generalizing $t=0$ Macdonald polynomials. We show that these polynomials are defined in terms of a vertex model, whose weights come not from an $R$-matrix, as is often the case, but from other intertwining operators of $U'_q(\hat{\mathfrak{sl}}_2)$-modules. Using this construction, we are able to prove a Cauchy-type identity for inhomogeneous spin $q$-Whittaker polynomials in full generality. Moreover, we are able to characterize spin $q$-Whittaker polynomials in terms of vanishing at certain points, and we find interpolation analogues of $q$-Whittaker and elementary symmetric polynomials.

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BibTeXRIS

Sergei Korotkikh. 2022-04-13. Representation theoretic interpretation and interpolation properties of inhomogeneous spin $q$-Whittaker polynomials. https://arxiv.org/abs/2204.06166

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