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SIGMA, 2020 Volume 16, 116, 55 pp. (Mi sigma1654)

This article is cited in 6 papers

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

Masayuki Fukudaa, Yusuke Ohkubob, Jun'ichi Shiraishib

a Department of Physics, Faculty of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033 Japan
b Graduate School of Mathematical Sciences, The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8914 Japan

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 $q \rightarrow 1$.

Keywords: Macdonald function, Rujisenaars function, Ding–Iohara–Miki algebra.

MSC: 33D52, 81R10

Received: April 23, 2020; in final form November 1, 2020; Published online November 18, 2020

Language: English

DOI: 10.3842/SIGMA.2020.116



Bibliographic databases:
ArXiv: 2002.00243


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