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Rationality of Eigenvalues of Cartan Matrices in Finite Groups

✍ Scribed by Masao Kiyota; Masafumi Murai; Tomoyuki Wada

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
101 KB
Volume
249
Category
Article
ISSN
0021-8693

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✦ Synopsis

We study the case in which eigenvalues and elementary divisors of a Cartan matrix of a p-block B of a finite group coincide. In several cases we prove the coincidence occurs if and only if the Perron-Frobenius eigenvalue of the Cartan matrix is equal to the order of a defect group of B.  2002 Elsevier Science (USA)

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