GL_{NM} quantum dynamical R-matrix based on solution of the associative Yang-Baxter equation
Abstract
In this letter we construct ${\rm GL}_{NM}$-valued dynamical $R$-matrix by means of unitary skew-symmetric solution of the associative Yang-Baxter equation in the fundamental representation of ${\rm GL}_{N}$. In $N=1$ case the obtained answer reproduces the ${\rm GL}_{M}$-valued Felder's $R$-matrix, while in the $M=1$ case it provides the ${\rm GL}_{N}$ $R$-matrix of vertex type including the Baxter-Belavin's elliptic one and its degenerations.
- Publication:
-
Russian Mathematical Surveys
- Pub Date:
- August 2019
- DOI:
- 10.1070/RM9897
- arXiv:
- arXiv:1905.08724
- Bibcode:
- 2019RuMaS..74..767S
- Keywords:
-
- 16T25;
- 81R12;
- Mathematics - Quantum Algebra;
- High Energy Physics - Theory;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 6 pages, minor changes