For t = q^{-m}, eigenfunctions from DIM Hamiltonians and twisted Cherednik Hamiltonians combine into identical symmetric functions that are eigenfunctions of both systems simultaneously.
A reproducing kernel for nonsymmetric Macdonald polynomials
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
We present a new formula of Cauchy type for the nonsymmetric Macdonald polynomials which are joint eigenfunctions of q-Dunkl operators. This gives the explicit formula for a reproducing kernel on the polynomial ring of n variables.
fields
hep-th 3years
2026 3representative 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.
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 automorphisms.
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.
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Integrable systems inspired by DAHA and DIM algebra: type $C^\vee C$ versus type $A$
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 automorphisms.