Finite-dimensional representations of the elliptic modular double

Abstract

We investigate the kernel space of an integral operator M(g) depending on the "spin" g and describing an elliptic Fourier transformation. The operator M(g) is an intertwiner for the elliptic modular double formed from a pair of Sklyanin algebras with the parameters $\eta$ and $\tau$, Im$\tau >0$, Im$\eta >0$. For two-dimensional lattices $g=n\eta +m\tau /2$ and $g=1/2+n\eta +m\tau /2$ with incommensurate $1,2\eta ,\tau$ and integers $n,m>0$, the operator M(g) has a finite-dimensional kernel that consists of the products of theta functions with two different modular parameters and is invariant under the action of generators of the elliptic modular double.

25 pp., published version

References in corpus (4)

• Yang-Baxter R operators and parameter permutations
• Baxter operators with deformed symmetry
• Ruijsenaars' hypergeometric function and the modular double of U_q(sl(2,C))
• Continuous biorthogonality of the elliptic hypergeometric function

Cited by in corpus (2)

• New elliptic solutions of the Yang-Baxter equation
• A duality web of linear quivers