English

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

Quantum Algebra 2021-10-06 v1 High Energy Physics - Theory Mathematical Physics math.MP Exactly Solvable and Integrable Systems

Abstract

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

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Cite

@article{arxiv.2104.04963,
  title  = {Quadratic algebras based on SL(NM) elliptic quantum R-matrices},
  author = {I. A. Sechin and A. V. Zotov},
  journal= {arXiv preprint arXiv:2104.04963},
  year   = {2021}
}

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10 pages