Semigroups and weights for group representations

Putcha, Mohan

doi:10.1090/S0002-9939-00-05464-2

Semigroups and weights for group representations
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by Mohan S. Putcha PDF

Proc. Amer. Math. Soc. 128 (2000), 2835-2842 Request permission

Abstract:

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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