On complete solution of the quantum Dell system
H. Awata, H. Kanno, A. Mironov, A. Morozov
TL;DR
This paper advances the explicit construction of the quantum double-elliptic (Dell) system by expressing its eigenfunctions as infinite series, addressing a long-standing problem in integrable systems.
Contribution
It provides a novel representation of the eigenfunctions for the quantum Dell Hamiltonians using infinite series in Miwa variables, linking to recent conjectures.
Findings
Eigenfunctions expressed as infinite series in Miwa variables
Connection to conjectures by J. Shiraishi
Progress towards explicit Dell system construction
Abstract
The mother functions for the eigenfunctions of the Koroteev-Shakirov version of quantum double-elliptic (Dell) Hamiltonians can be presented as infinite series in Miwa variables, very similar to the recent conjecture due to J. Shiraishi. Further studies should clear numerous remaining obstacles and thus solve the long-standing problem of explicitly constructing a Dell system, the top member of the Calogero-Moser-Ruijsenaars system, with the -duality fully explicit at the elliptic level.
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