For t = q^{-m}, eigenfunctions from DIM Hamiltonians and twisted Cherednik Hamiltonians combine into identical symmetric functions that are eigenfunctions of both systems simultaneously.
Twisted Cherednik spectrum as a $q,t$-deformation
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The common eigenfunctions of the twisted Cherednik operators can be first analyzed in the limit of $q\longrightarrow 1$. Then, the polynomial eigenfunctions form a simple set originating from the symmetric ground state of non-vanishing degree and excitations over it, described by non-symmetric polynomials of higher degrees and enumerated by weak compositions. This pattern is inherited by the full spectrum at $q\neq 1$, which can be considered as a deformation. The whole story looks like a typical NP problem: the Cherednik equations are difficult to solve, but easy to check the solution once it is somehow found.
fields
hep-th 2years
2026 2representative citing papers
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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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.