Cartan matrices and Brauer’s k(B)-conjecture III

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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  • Benjamin Sambale

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  • Friedrich-Schiller-Universität Jena
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OriginalspracheEnglisch
Seiten (von - bis)505-518
Seitenumfang14
FachzeitschriftManuscripta mathematica
Jahrgang146
Ausgabenummer3-4
PublikationsstatusVeröffentlicht - März 2014

Abstract

For a block B of a finite group we prove that (Formula presented.) where k(B) [respectively l(B)] is the number of irreducible ordinary (respectively Brauer) characters of B, and C is the Cartan matrix of B. As an application, we show that Brauer’s k(B)-Conjecture holds for every block with abelian defect group D and inertial quotient T provided there exists an element u ∈ D such that CT(u) acts freely on (Formula presented.). This gives a new proof of Brauer’s Conjecture for abelian defect groups of rank at most 2. We also prove the conjecture in case (Formula presented.).

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Cartan matrices and Brauer’s k(B)-conjecture III. / Sambale, Benjamin.
in: Manuscripta mathematica, Jahrgang 146, Nr. 3-4, 03.2014, S. 505-518.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Sambale B. Cartan matrices and Brauer’s k(B)-conjecture III. Manuscripta mathematica. 2014 Mär;146(3-4):505-518. doi: 10.1007/s00229-014-0702-x
Sambale, Benjamin. / Cartan matrices and Brauer’s k(B)-conjecture III. in: Manuscripta mathematica. 2014 ; Jahrgang 146, Nr. 3-4. S. 505-518.
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