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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Groups of linear operators defined by group characters


Authors: Marvin Marcus and James Holmes
Journal: Trans. Amer. Math. Soc. 172 (1972), 177-194
MSC: Primary 20G05
MathSciNet review: 0310081
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Abstract: Some of the recent work on invariance questions can be regarded as follows: Characterize those linear operators on $ \operatorname{Hom} (V,V)$ which preserve the character of a given representation of the full linear group. In this paper, for certain rational characters, necessary and sufficient conditions are described that ensure that the set of all such operators forms a group $ \mathfrak{L}$. The structure of $ \mathfrak{L}$ is also determined. The proofs depend on recent results concerning derivations on symmetry classes of tensors.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0310081-9
PII: S 0002-9947(1972)0310081-9
Keywords: Representations, characters, linear transformations, elementary divisors, symmetry classes of tensors, derivations on symmetry classes
Article copyright: © Copyright 1972 American Mathematical Society