Matrix Bailey Lemma and the Star-Triangle Relation

Symmetry Integrability and Geometry-Methods and Applications

article

Kamil Yu. Magadov¹  Vyacheslav P. Spiridonov² 

[1] Moscow Institute of Physics and Technology;Laboratory of Theoretical Physics

关键词: elliptic hypergeometric functions;    Bailey lemma;    star-triangle relation;   

DOI  :  10.3842/SIGMA.2018.121

来源: National Academy of Science of Ukraine

【 摘 要 】

We compare previously found finite-dimensional matrix and integral operator realizations of the Bailey lemma employing univariate elliptic hypergeometric functions. With the help of residue calculus we explicitly show how the integral Bailey lemma can be reduced to its matrix version. As a consequence, we demonstrate that the matrix Bailey lemma can be interpreted as a star-triangle relation, or as a Coxeter relation for a permutation group.

【 授权许可】

Unknown