Almost Commutative Terwilliger Algebras II: Strong Gelfand Pairs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915503258206208 |
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| author | Bastian, Nicholas L. Humphries, Stephen P. |
| author_facet | Bastian, Nicholas L. Humphries, Stephen P. |
| contents | Terwilliger algebras are a subalgebra of a matrix algebra constructed from an association scheme. In 2010, Tanaka defined what it means for a Terwilliger algebra to be almost commutative and gave five equivalent conditions for a Terwilliger algebra to be almost commutative. In this paper we look at Terwilliger algebras coming from strong Gelfand pairs $(G,H)$ for a finite group $G$. From such a pair, one can create a Terwilliger algebra using the Schur ring of $H-$classes of elements of $G$. We determine all strong Gelfand pairs that give an Almost Commutative Terwilliger algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_16174 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost Commutative Terwilliger Algebras II: Strong Gelfand Pairs Bastian, Nicholas L. Humphries, Stephen P. Representation Theory Combinatorics Rings and Algebras 05E30, 05E16 Terwilliger algebras are a subalgebra of a matrix algebra constructed from an association scheme. In 2010, Tanaka defined what it means for a Terwilliger algebra to be almost commutative and gave five equivalent conditions for a Terwilliger algebra to be almost commutative. In this paper we look at Terwilliger algebras coming from strong Gelfand pairs $(G,H)$ for a finite group $G$. From such a pair, one can create a Terwilliger algebra using the Schur ring of $H-$classes of elements of $G$. We determine all strong Gelfand pairs that give an Almost Commutative Terwilliger algebra. |
| title | Almost Commutative Terwilliger Algebras II: Strong Gelfand Pairs |
| topic | Representation Theory Combinatorics Rings and Algebras 05E30, 05E16 |
| url | https://arxiv.org/abs/2509.16174 |