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arXiv · 2512.24811

Twisted Cherednik systems and non-symmetric Macdonald polynomials

A. Mironov·A. Morozov·A. Popolitov
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Abstract

We consider eigenfunctions of many-body system Hamiltonians associated with generalized (a-twisted) Cherednik operators used in construction of other Hamiltonians: those arising from commutative subalgebras of the Ding-Iohara-Miki (DIM) algebra. The simplest example of these eigenfunctions is provided by non-symmetric Macdonald polynomials, while generally they are constructed basing on the ground state eigenfunction coinciding with the twisted Baker-Akhiezer function being a peculiar (symmetric) eigenfunction of the DIM Hamiltonians. Moreover, the eigenfunctions admit an expansion with universal coefficients so that the dependence on the twist $a$ is hidden only in these ground state eigenfunctions, and we suggest a general formula that allows one to construct these eigenfunctions from non-symmetric Macdonald polynomials. This gives a new twist in theory of integrable systems, which usually puts an accent on symmetric polynomials, and provides a new dimension to the {\it triad} made from the symmetric Macdonald polynomials, untwisted Baker-Akhiezer functions and Noumi-Shiraishi series.

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A. Mironov, A. Morozov, A. Popolitov. 2025-12-31. Twisted Cherednik systems and non-symmetric Macdonald polynomials. https://arxiv.org/abs/2512.24811

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