Description of the Characters and Factor Representations of Infinite Symmetric Inverse Semigroup

Abstract

We give a complete list of indecomposable characters of the infinite symmetric semigroup. In comparison with the analogous list for the infinite symmetric group, one should introduce only one new parameter, which has a clear combinatorial meaning. The paper relies on the representation theory of the finite symmetric semigroups and the representation theory of the infinite symmetric group.

13 pp. Ref. 21; Func.Anal. and Appl. No 1, 2011