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arXiv · 2510.23173

A skew group ring of $\mathbb Z/2\mathbb Z$ over $U(\mathfrak{sl}_2)$, Leonard triples and odd graphs

Hau-Wen Huang·Chin-Yen Lee
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Abstract

We employ a skew group ring of $\mathbb Z/2\mathbb Z$ over $U(\mathfrak{sl}_2)$ to construct modules over the universal Bannai--Ito algebra. In addition, we give the conditions under which the defining generators act as Leonard triples on the resulting modules. As a combinatorial realization, we establish an algebra homomorphism from the universal Bannai--Ito algebra onto the Terwilliger algebra of an odd graph. This homomorphism provides a unified description of Leonard triples on all irreducible modules over the Terwilliger algebra.

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Hau-Wen Huang, Chin-Yen Lee. 2025-10-27. A skew group ring of $\mathbb Z/2\mathbb Z$ over $U(\mathfrak{sl}_2)$, Leonard triples and odd graphs. https://arxiv.org/abs/2510.23173

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