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

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