Description of the Characters and Factor Representations of Infinite   Symmetric Inverse Semigroup
  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. 
Anatoly Vershik, Pavel Nikitin
math.RT math.CO