Studies in the representation theory of finite semigroups
Author:
Yechezkel Zalcstein
Journal:
Trans. Amer. Math. Soc. 161 (1971), 7187
MSC:
Primary 20.90
MathSciNet review:
0283104
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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 of U, can be ``extended'' formally to an irreducible character of S. This yields a partial generalization of a wellknown theorem of Frobenius on the characters of multiplytransitive 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.
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 John Rhodes and Y. Zalcstein, Elementary representation and character theory of finite semigroups and its applications, Advances in Math. (to appear). MR 1142387 (92k:20129)
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 Bret Tilson, Complexity of two class semigroups, Advances in Math. (to appear).
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DOI:
http://dx.doi.org/10.1090/S00029947197102831042
PII:
S 00029947(1971)02831042
Keywords:
Finite semigroup,
irreducible representation,
character,
Ktransitive
Article copyright:
© Copyright 1971
American Mathematical Society
