Elliptic triad

A. Mironov; A. Morozov; A. Popolitov; Z. Zakirova

Elliptic triad

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arxiv 2412.19588 v2 pith:UZ2DB5CY submitted 2024-12-27 hep-th math-phmath.MP

Elliptic triad

A. Mironov , A. Morozov , A. Popolitov , Z. Zakirova This is my paper

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keywords elliptictriaddiscussequationsfunctionslinearmacdonaldnoumi-shiraishi

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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Integrable systems inspired by DAHA and DIM algebra: type $C^\vee C$ versus type $A$
hep-th 2026-07 accept novelty 4.5

Type C∨C DAHA and Koornwinder systems mirror type-A Macdonald structures for Hamiltonians, recursions, evaluations and dualities, but lack a usable Noumi-Shiraishi-style universal series and SL(2,Z)-type twisting auto...