On complete solution of the quantum Dell system

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 $PQ$-duality fully explicit at the elliptic level.

arXiv comment22 pages

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Cited by in corpus (11)

• Duality in elliptic Ruijsenaars system and elliptic symmetric functions
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Basic Properties of Non-Stationary Ruijsenaars Functions
• On Chalykh's approach to eigenfunctions of DIM-induced integrable Hamiltonians
• Characteristic determinant and Manakov triple for the double elliptic integrable system
• Energy-Energy Correlator from the AdS Virasoro-Shapiro Amplitude
• On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta
• Diamond of triads
• Elliptic triad
• Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation
• Twisted Baker-Akhiezer function from determinants