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Semigroups and weights for group representations

Author: Mohan S. Putcha
Journal: Proc. Amer. Math. Soc. 128 (2000), 2835-2842
MSC (2000): Primary 20C99, 20M30
Published electronically: March 2, 2000
MathSciNet review: 1691001
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Let $G$ be a finite group. Consider a pair $\chi=(\chi_+,\chi_-)$ of linear characters of subgroups $P,P^-$ of $G$ with $\chi_+$ and $\chi_-$ agreeing on $P\cap P^-$. Naturally associated with $\chi$ is a finite monoid $M_\chi$. Semigroup representation theory then yields a representation $\theta$ of $G$. If $\theta$ is irreducible, we say that $\chi$ is a weight for $\theta$. When the underlying field is the field of complex numbers, we obtain a formula for the character of $\theta$ in terms of $\chi_+$ and $\chi_-$. We go on to construct weights for some familiar group representations.

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Additional Information

Mohan S. Putcha
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205

Received by editor(s): November 1, 1998
Published electronically: March 2, 2000
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 2000 American Mathematical Society

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