Non-Stationary Ruijsenaars Functions for $\kappa=t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra
| Autor: | Jun'ichi Shiraishi, Masayuki Fukuda, Yusuke Ohkubo |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
010102 general mathematics Elliptic hypergeometric series Conformal map 01 natural sciences Fock space Algebra Lift (mathematics) Operator (computer programming) Mathematics::Quantum Algebra 0103 physical sciences Mathematics - Quantum Algebra 010307 mathematical physics Geometry and Topology Affine transformation 0101 mathematics Algebraic number Analysis Kappa Mathematical Physics Mathematics |
| Popis: | 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 $q \rightarrow 1$. |
| Databáze: | OpenAIRE |
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