I. A. Sechin, A. V. Zotov, “Quadratic algebras based on $SL(NM)$ elliptic quantum $R$-matrices”, TMF, 2021, Volume 208, Number 2,Pages 355

This article is cited in 3 papers

Quadratic algebras based on $SL(NM)$ elliptic quantum $R$-matrices

I. A. Sechin^ab, A. V. Zotov^ac

^a National Research University "Higher School of Economics", Moscow, Russia
^b Center for Advanced Studies, Skolkovo Institute of Science and Technology, Moscow, Russia
^c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We construct a quadratic quantum algebra based on the dynamical $RLL$-relation for the quantum $R$-matrix related to $SL(NM)$-bundles with a nontrivial characteristic class over an elliptic curve. This $R$-matrix simultaneously generalizes the elliptic nondynamical Baxter–Belavin and the dynamical Felder $R$-matrices, and the obtained quadratic relations generalize both the Sklyanin algebra and the relations in the Felder–Tarasov–Varchenko elliptic quantum group, which are reproduced in the respective particular cases $M=1$ and $N=1$.

Keywords: quantum quadratic algebras, elliptic integrable system, quantum dynamical $R$-matrix.

Received: 25.03.2021
Revised: 25.03.2021

DOI: 10.4213/tmf10100