Bijection between Conjugacy Classes and Irreducible Representations of Finite Inverse Semigroups

2012/08/28 by Zhenheng Li, Zhuo Li, Li, Zhenheng +1
Computer Science · Mathematics · #20M18 #20M32 #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20M18 #msc:20M32 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1208.5735

arxiv created 2012/08/28 · openalex publication_date 2012/08/28 · arxiv updated 2012/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that the irreducible representations of a finite inverse semigroup S over an algebraically closed field F are in bijection with the conjugacy classes of S if the characteristic of F is zero or a prime number that does not divide the order of any maximal subgroup of S.

Citations

• On conjugacy in regular epigroups

Related

• Some conditions from a finite regular semigroup to a finite inverse semigroup
• Membership and Conjugacy in Inverse Semigroups
• On Isometric Representations of the Perforated Semigroup
• A Groupoid Approach to Discrete Inverse Semigroup Algebras
• Primer on inverse semigroups II