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Autores principales:	Huang, Hau-Wen, Lee, Chin-Yen
Formato:	Preprint
Publicado:	2025
Materias:	Combinatorics Representation Theory 05E10, 05E30, 16S35, 33D45
Acceso en línea:	https://arxiv.org/abs/2510.23173
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

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author	Huang, Hau-Wen Lee, Chin-Yen
author_facet	Huang, Hau-Wen Lee, Chin-Yen
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2510_23173
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	A skew group ring of $\mathbb Z/2\mathbb Z$ over $U(\mathfrak{sl}_2)$, Leonard triples and odd graphs Huang, Hau-Wen Lee, Chin-Yen Combinatorics Representation Theory 05E10, 05E30, 16S35, 33D45 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.
title	A skew group ring of $\mathbb Z/2\mathbb Z$ over $U(\mathfrak{sl}_2)$, Leonard triples and odd graphs
topic	Combinatorics Representation Theory 05E10, 05E30, 16S35, 33D45
url	https://arxiv.org/abs/2510.23173

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