On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians

Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at t=q−m to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreo...

Full description

Saved in:
Bibliographic Details
Main Authors: A. Mironov, A. Morozov, A. Popolitov
Format: Article
Language:English
Published: Elsevier 2025-04-01
Series:Physics Letters B
Online Access:http://www.sciencedirect.com/science/article/pii/S0370269325001406
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at t=q−m to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg Chalykh suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the (−1,a) rays of the Ding-Iohara-Miki algebra. In the paper, we discuss this suggestion and some evidence in its support.
ISSN:0370-2693