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Non-Stationary Ruijsenaars Functions for $\kappa=t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra

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arxiv 2002.00243 v3 pith:ZYPYVDOD submitted 2020-02-01 math.QA hep-thmath-phmath.MP

Masayuki Fukuda , Yusuke Ohkubo , Jun'ichi Shiraishi This is my paper · ORCID
classification math.QAhep-thmath-phmath.MP
keywords functionsalgebraruijsenaarselliptickappanon-stationaryoperatoroperators
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abstract

We construct the non-stationary Ruijsenaars functions (affine analogue of the Macdonald functions) in the special case $\kappa=t^{-1/N}$, using the intertwining operators of the Ding-Iohara-Miki algebra (DIM algebra) associated with $N$-fold Fock tensor spaces. By the $S$-duality of the intertwiners, another expression is obtained for the non-stationary Ruijsenaars functions with $\kappa=t^{-1/N}$, which can be regarded as a natural elliptic lift of the asymptotic Macdonald functions to the multivariate elliptic hypergeometric series. We also investigate some properties of the vertex operator of the DIM algebra appearing in the present algebraic framework; an integral operator which commutes with the elliptic Ruijsenaars operator, and the degeneration of the vertex operators to the Virasoro primary fields in the conformal limit $q \rightarrow 1$.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Spiralling branes, affine qq-characters and elliptic integrable systems

    hep-th 2024-12 accept novelty 7.0 of 10

    Quantum toroidal algebra intertwiners reproduce Ruijsenaars-Schneider and Koroteev-Shakirov Hamiltonians, Shiraishi functions, and a new proof of the noncommutative Jacobi identity for affine qq-characters.

  2. A basic triad in Macdonald theory

    hep-th 2024-11 conditional novelty 6.0 of 10

    At t=q^{-m}, the Noumi-Shiraishi series reproduces the Baker-Akhiezer function, completing a triad with the Macdonald polynomials.

  3. Integrable systems inspired by DAHA and DIM algebra: type $C^\vee C$ versus type $A$

    hep-th 2026-07 accept novelty 4.5 of 10

    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 auto...

  4. Elliptic triad

    hep-th 2024-12 conditional novelty 4.0 of 10

    The paper argues that the Macdonald triad admits elliptic deformations, but the defining linear equations for elliptic Baker-Akhiezer functions remain ambiguous except at m=1.

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