Year: 2025
Type: preprint
Abstract: We study tridiagonal pairs of type II. These involve two linear transformations $A$ and $A^\star$. We define two bases. In the first one, $A$ acts as a diagonal matrix while $A^\star$ acts as a block tridiagonal matrix, and in the second one, $A$ acts as a block tridiagonal matrix while $A^\star$ 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.
Source: arXiv (Cornell University)
Authors: Crampe, Nicolas, Gaboriaud, Julien, Tsujimoto, Satoshi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979311704
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