An elliptic generalization of Cherednik-Macdonald-Mehta identities is introduced using Shiraishi functions, with an elliptic matrix model and a proof to first order in the elliptic parameter.
On Cherednik-Macdonald-Mehta identities
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
In this note we give a short proof of Cherednik's generalization of Macdonald-Mehta identities for the root system $A_{n-1}$ using the representation theory of quantum groups. These identities, suggested and proved by Cherednik, give an explicit formula for the integral of a product of Macdonald polynomials with respect to a ``difference analogue of the Gaussian measure''.
citation-role summary
background 1
citation-polarity summary
years
2026 3roles
background 1polarities
background 1representative 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.
Refined Chern-Simons theory universality is restricted to simply laced Lie groups, unlike the original which applies to all simple Lie groups.
citing papers explorer
-
Elliptic Generalization of Cherednik-Macdonald-Mehta identities
An elliptic generalization of Cherednik-Macdonald-Mehta identities is introduced using Shiraishi functions, with an elliptic matrix model and a proof to first order in the elliptic parameter.
-
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.
-
A note on universality in refined Chern-Simons theory
Refined Chern-Simons theory universality is restricted to simply laced Lie groups, unlike the original which applies to all simple Lie groups.