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arXiv · 2412.19588

Elliptic triad

A. Mironov·A. Morozov·A. Popolitov·Z. Zakirova
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Abstract

The triad refers to embedding the Macdonald polynomials into the Noumi-Shiraishi functions and their reduction to solutions of simple linear equations at particular values of $t$. It provides an alternative definition of Macdonald theory. We discuss lifting the triad to an elliptic generalization of the Noumi-Shiraishi functions. The central unknown ingredient is linear equations, for which we discuss various possible approaches, including immediate elliptic deformation of periodicity conditions, (elliptic) Ding-Iohara-Miki algebra operators, and elliptic Kostka coefficients.

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A. Mironov, A. Morozov, A. Popolitov, Z. Zakirova. 2024-12-27. Elliptic triad. https://doi.org/10.1016/j.physletb.2025.139467

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