For t = q^{-m}, eigenfunctions from DIM Hamiltonians and twisted Cherednik Hamiltonians combine into identical symmetric functions that are eigenfunctions of both systems simultaneously.
Macdonald polynomials and algebraic integrability
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We construct explicitly non-polynomial eigenfunctions of the difference operators by Macdonald in case $t=q^k$, $k\in{\mathbb Z}$. This leads to a new, more elementary proof of several Macdonald conjectures, first proved by Cherednik. We also establish the algebraic integrability of Macdonald operators at $t=q^k$ ($k\in {\mathbb Z}$), generalizing the result of Etingof and Styrkas. Our approach works uniformly for all root systems including $BC_n$ case and related Koornwinder polynomials. Moreover, we apply it for a certain deformation of $A_n$ root system where the previously known methods do not work.
fields
hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The twisted Cherednik spectrum is a q,t-deformation of the polynomial eigenfunctions built from symmetric ground states and weak-composition excitations at q=1.
citing papers explorer
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Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems
For t = q^{-m}, eigenfunctions from DIM Hamiltonians and twisted Cherednik Hamiltonians combine into identical symmetric functions that are eigenfunctions of both systems simultaneously.
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Twisted Cherednik spectrum as a $q,t$-deformation
The twisted Cherednik spectrum is a q,t-deformation of the polynomial eigenfunctions built from symmetric ground states and weak-composition excitations at q=1.