Bijection between Conjugacy Classes and Irreducible Representations of   Finite Inverse Semigroups
  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 $S$. 
Zhenheng Li, Zhuo Li
math.RT