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 $q$-analogue of the type $A$ Dunkl operator and integral kernel
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abstract
We introduce the $q$-analogue of the type $A$ Dunkl operators, which are a set of degree--lowering operators on the space of polynomials in $n$ variables. This allows the construction of raising/lowering operators with a simple action on non-symmetric Macdonald polynomials. A bilinear series of non-symmetric Macdonald polynomials is introduced as a $q$-analogue of the type $A$ Dunkl integral kernel ${\cal K}_A(x;y)$. The aforementioned operators are used to show that the function satisfies $q$-analogues of the fundamental properties of ${\cal K}_A(x;y)$.
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.