On algebras of conjugacy classes of symmetric groups with respect to Young subgroups

2025/09/08 by Neretin, Yury A.
Mathematics · #14H57 #14H573 #20B30 #20C05 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2509.07148

openalex publication_date 2025/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the subalgebra of the group algebra of a symmetric group consisting of functions that are constant on conjugacy classes with respect to a Young subgroup. We write an expression for structure constants of this algebra in the spirit of Hurwitz numbers.

Citations

• An introduction to the symmetric group algebra
• Algebra of double cosets of a symmetric group by a smaller symmetric group
• Virtual permutations and polymorhisms
• Hurwitz numbers from matrix integrals over Gaussian measure
• The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations

Related

• The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations
• An introduction to the symmetric group algebra
• Sign conjugacy classes in symmetric groups
• Algebra of double cosets of a symmetric group by a smaller symmetric group
• Lie Elements and Knuth Relations