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arXiv · 2606.12796

Rank recursion for $q$-Whittaker and Macdonald operators

Philippe Di Francesco·Hieu Trung Vu
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Abstract

In this paper, we introduce and prove a set of rank recurrence relations for $q$-Whittaker and Macdonald operators. We also derive an explicit expression for the $k$-th power of the $q$-Whittaker operators in terms of the $q$-deformed binomial probability distribution, and we express the rank recurrence relations for the Macdonald operators in terms of the Cauchy determinant.

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BibTeXRIS

Philippe Di Francesco, Hieu Trung Vu. 2026-06-11. Rank recursion for $q$-Whittaker and Macdonald operators. https://arxiv.org/abs/2606.12796

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