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

Bijection between Conjugacy Classes and Irreducible Representations of Finite Inverse Semigroups