Geodesic
Description of the Characters and Factor Representations of the Infinite Symmetric Inverse Semigroup
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 16-30.

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A complete list of indecomposable characters of the infinite symmetric semigroup is given. In comparison with a similar list for the infinite symmetric group, only one new parameter appears, which has a clear combinatorial meaning. The results rely on the representation theory of finite symmetric semigroups and the representation theory of the infinite symmetric group.
Keywords: symmetric semigroup, character, factor representation, infinite symmetric group. 
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A. M. Vershik; P. P. Nikitin. Description of the Characters and Factor Representations of the Infinite Symmetric Inverse Semigroup. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 16-30. http://geodesic.mathdoc.fr/item/FAA_2011_45_1_a1/

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