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arXiv · 2503.01231

Change of basis for the tridiagonal pairs of type II

Nicolas Crampe·Julien Gaboriaud·Satoshi Tsujimoto
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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.

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Nicolas Crampe, Julien Gaboriaud, Satoshi Tsujimoto. 2025-03-03. Change of basis for the tridiagonal pairs of type II. https://arxiv.org/abs/2503.01231

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