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Recently we found Mellin-Barnes integrals, representing the wave function for $GL(n,mathbb{R})$ hyperbolic Sutherland model. In present paper, we establish bispectral properties of this wave function with respect to dual Ruijesenaars-Macdonald operators.
We obtain certain Mellin-Barnes integrals which present wave functions for $GL(n,mathbb{R})$ hyperbolic Sutherland model with arbitrary positive coupling constant.
Let $mathsf k$ be a local field. Let $I_ u$ and $I_{ u}$ be smooth principal series representations of $mathrm{GL}_n(mathsf k)$ and $mathrm{GL}_{n-1}(mathsf k)$ respectively. The Rankin-Selberg integrals yield a continuous bilinear map $I_ utimes I_{
Let $W_{m|n}$ be the (finite) $W$-algebra attached to the principal nilpotent orbit in the general linear Lie superalgebra $mathfrak{gl}_{m|n}(mathbb{C})$. In this paper we study the {em Whittaker coinvariants functor}, which is an exact functor from
In this paper, we used the free fields of Wakimoto to construct a class of irreducible representations for the general linear Lie superalgebra $mathfrak{gl}_{m|n}(mathbb{C})$. The structures of the representations over the general linear Lie superalg
In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F. We study r