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

Abstract

We construct quadratic quantum algebra based on the dynamical RLL-relation for the quantum $R$-matrix related to $SL(NM)$-bundles with nontrivial characteristic class over elliptic curve. This $R$-matrix generalizes simultaneously 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 particular cases $M=1$ and $N=1$ respectively.

10 pages

References in corpus (2)

• Relativistic interacting integrable elliptic tops
• Quadratic algebras related to elliptic curves

Cited by in corpus (2)

• Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and R-matrix identities
• Lax equations for relativistic $\mathrm{GL}(NM,\mathbb{C})$ Gaudin models on elliptic curve