Non-Stationary Ruijsenaars Functions for κ=t−1/N and Intertwining Operators of Ding-Iohara-Miki Algebra
Non-Stationary Ruijsenaars Functions for κ=t−1/N and Intertwining Operators of Ding-Iohara-Miki Algebra
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DOI：
10.3842/sigma.2020.116
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发表时间：
2020-02
影响因子：
0.9
通讯作者：
M. Fukuda;Y. Ohkubo;J. Shiraishi
中科院分区：
文献类型：
--
作者：
M. Fukuda;Y. Ohkubo;J. Shiraishi
利用与$N$-fold Fock张量空间相关联的Ding-Iohara-三木代数（DIM代数）的交织算子，构造了$\kappa=t^{-1/N}$情形下的非平稳Ruijsenaars函数（Macdonald函数的仿射模拟）.利用缠绕子的S-对偶性，得到了满足$\kappa=t^{-1/N}$的非平稳Ruijsenaars函数的另一个表达式，它可以看作是渐近Macdonald函数到多元椭圆超几何级数的一个自然椭圆提升.我们还调查了一些性质的顶点运营商的DIM代数出现在本代数的框架;积分算子与椭圆型Ruijsenaars运营商，和退化的顶点运营商的Virasoro主要领域的共形限制$q \rightarrow 1$。
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 $q \rightarrow 1$.