Studies in the representation theory of finite semigroups
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- by Yechezkel Zalcstein PDF
- Trans. Amer. Math. Soc. 161 (1971), 71-87 Request permission
Abstract:
This paper is a continuation of [14], developing the representation theory of finite semigroups further. The main result, Theorem 1.24, states that if the group of units U of a mapping semigroup (X, S) is multiply transitive with a sufficiently high degree of transitivity, then for certain irreducible characters $\chi$ of U, $\chi$ can be “extended” formally to an irreducible character of S. This yields a partial generalization of a well-known theorem of Frobenius on the characters of multiply-transitive groups and provides the first nontrivial explicit formula for an irreducible character of a finite semigroup. The paper also contains preliminary results on the “spectrum” (i.e., the set of ranks of the various elements) of a mapping semigroup.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 161 (1971), 71-87
- MSC: Primary 20.90
- DOI: https://doi.org/10.1090/S0002-9947-1971-0283104-2
- MathSciNet review: 0283104