Geodesic
Finite-dimensional representations of the elliptic modular double
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 177-201 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the kernel space of an integral operator $\mathrm M(g)$ depending on the "spin" $g$ and describing an elliptic Fourier transformation. The operator $\mathrm M(g)$ is an intertwiner for the elliptic modular double formed from a pair of Sklyanin algebras with the parameters $\eta$ and $\tau$, $\operatorname{Im}\tau>0$, $\operatorname{Im}\eta>0$. 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 $\mathrm M(g)$ 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.
Keywords: Yang–Baxter equation, elliptic modular double, elliptic hypergeometric function. 
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S. È. Derkachev; V. P. Spiridonov. Finite-dimensional representations of the elliptic modular double. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 177-201. http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a1/

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