2025/09/19 by Nicholas Bastian, Bastian, Nicholas L., Stephen P. Humphries +1 · 1 citation
Mathematics · #05E16 #05E30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2509.16174
openalex publication_date 2025/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.