Change of basis for tridiagonal pairs of type II - Nicolas Crampé; Julien Gaboriaud; Satoshi Tsujimoto (Nuclear Physics B)
This paper is on the topic of tridiagonal pairs of type II. These involve two linear transformations A and A⋆. We define two bases. In the first one, A acts as a diagonal matrix while A⋆ acts as a block tridiagonal matrix, and in the second one, A acts as a block tridiagonal matrix while A⋆ acts as a diagonal matrix. We obtain the change of basis coefficients between these two bases. The coefficients are special functions that are written as a nested product of polynomials that resemble Racah polynomials but involve shift operators in their expression.