Finite-dimensional representations of the~elliptic modular double
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 177-201
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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.
@article{TMF_2015_183_2_a1,
author = {S. \`E. Derkachev and V. P. Spiridonov},
title = {Finite-dimensional representations of the~elliptic modular double},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {177--201},
publisher = {mathdoc},
volume = {183},
number = {2},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a1/}
}
TY - JOUR AU - S. È. Derkachev AU - V. P. Spiridonov TI - Finite-dimensional representations of the~elliptic modular double JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2015 SP - 177 EP - 201 VL - 183 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a1/ LA - ru ID - TMF_2015_183_2_a1 ER -
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/