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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Semigroups and weights for group representations
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by Mohan S. Putcha
Proc. Amer. Math. Soc. 128 (2000), 2835-2842
DOI: https://doi.org/10.1090/S0002-9939-00-05464-2
Published electronically: March 2, 2000

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.
References
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Bibliographic Information
  • Mohan S. Putcha
  • Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
  • Email: putcha@math.ncsu.edu
  • Received by editor(s): November 1, 1998
  • Published electronically: March 2, 2000
  • Communicated by: Ronald M. Solomon
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 2835-2842
  • MSC (2000): Primary 20C99, 20M30
  • DOI: https://doi.org/10.1090/S0002-9939-00-05464-2
  • MathSciNet review: 1691001