${\rm SL}(2,\mathbb{C})$ Gustafson Integrals

Symmetry Integrability and Geometry-Methods and Applications

article

Sergey É. Derkachov¹  Alexander N. Manashov²  Pavel A. Valinevich¹ 

[1] Saint-Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences;Institut f¨ur Theoretische Physik

关键词: Baxter operators;    separation of variables;   

DOI  :  10.3842/SIGMA.2018.030

来源: National Academy of Science of Ukraine

【 摘 要 】

It was shown recently that many of the Gustafson integrals appear in studies of the ${\rm SL}(2,\mathbb{R})$ spin chain models. One can hope to obtain a generalization of the Gustafson integrals considering spin chain models with a different symmetry group. In this paper we analyse the spin magnet with the ${\rm SL}(2,\mathbb{C})$ symmetry group in case of open and periodic boundary conditions and derive several new integrals.

【 授权许可】

Unknown