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Description of the characters and factor representations of the infinite symmetric inverse semigroup. (English. Russian original) Zbl 1271.20072
Funct. Anal. Appl. 45, No. 1, 13-24 (2011); translation from Funkts. Anal. Prilozh. 45, No. 1, 16-30 (2011).
Summary: 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.

MSC:
20M30 Representation of semigroups; actions of semigroups on sets
20M20 Semigroups of transformations, relations, partitions, etc.
20C32 Representations of infinite symmetric groups
20M18 Inverse semigroups
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