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

TL;DR

This paper constructs a new quadratic quantum algebra based on an elliptic R-matrix related to SL(NM) bundles, generalizing several known algebraic structures in quantum integrable systems.

Contribution

It introduces a novel quadratic algebra derived from a dynamical R-matrix that unifies and extends existing elliptic quantum algebras.

Findings

Generalizes Sklyanin algebra and Felder-Tarasov-Varchenko elliptic quantum group

Reproduces known algebras in special cases M=1 and N=1

Provides a framework for elliptic quantum algebras on SL(NM) bundles

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.