Algebra of double cosets of a symmetric group by a smaller symmetric group

2025/06/20 by Neretin, Yury A. · 2 citations
Mathematics · #20B30 #20C05 #20C30 #20N20 #Advanced Combinatorial Mathematics #Algebraic and Geometric Analysis #FOS: Mathematics #Group Theory (math.GR) #Holomorphic and Operator Theory #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2506.17069

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fix a natural α. Let n≥ α be an integer. Consider the symmetric group S_α+n and its subgroup S_n. We consider the group algebra of S_α+n and its subalgebra \mathbbO[α;n] consisting of S_n-biinvariant functions, i.e., functions, which are constant on double cosets of S_α+n with respect to S_n. We obtain two simple descriptions of \mathbbO[α;n]. First, we write explicitly formulas for multiplication in a natural basis (structure constants are Pochhammer symbols). Secondly, we describe this algebra in terms of generators and relations. We also construct an interpolating family of algebras \mathbbO[α;ν] depending on a complex parameter ν.

Citations

• One algebra of double cosets for a general linear group over a finite field
• Stable Centres II: Finite Classical Groups
• Partial isomorphisms over finite fields

Cited by

• On algebras of conjugacy classes of symmetric groups with respect to Young subgroups
• One algebra of double cosets for a general linear group over a finite field

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