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On complete solution of the quantum Dell system

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arxiv 1912.12897 v3 pith:3JXQLSGQ submitted 2019-12-30 hep-th math-phmath.MP

On complete solution of the quantum Dell system

classification hep-th math-phmath.MP
keywords dellsystemquantumcalogero-moser-ruijsenaarsclearcompleteconjectureconstructing
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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