2025/03/03 by Crampe, Nicolas, Gaboriaud, Julien, Tsujimoto, Satoshi
#16G60 #33C50 #33C80 #47B36 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2503.01231
We study 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.