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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Character values of finite groups as eigenvalues of nonnegative integer matrices


Author: David Chillag
Journal: Proc. Amer. Math. Soc. 97 (1986), 565-567
MSC: Primary 20C15
MathSciNet review: 840647
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Abstract: Let $ {C_1}$, $ {C_2}, \ldots $, $ {C_k}$ be the conjugacy classes of the finite group $ G$ and choose $ {x_i} \in {C_i}$, for $ i = 1$, $ 2, \ldots $, $ k$. For every complex character $ \theta $ of $ G$ there is a $ k \times k$ matrix $ M(\theta )$ whose entries are nonnegative integers such that $ {X^{ - 1}}M(\theta )X = {\text{diag}}(\theta ({x_1}),\theta ({x_2}), \ldots ,\theta ({x_k}))$ where $ X$ is the character table matrix of $ G$. Some consequences are shown.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0840647-4
PII: S 0002-9939(1986)0840647-4
Article copyright: © Copyright 1986 American Mathematical Society