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Arithmetical Properties of Blocks

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Algebraic Groups and their Representations

Part of the book series: NATO ASI Series ((ASIC,volume 517))

Abstract

Richard Brauer began the development of the theory of modular representations of finite groups, and one of his main motivations was to obtain arithmetical information about complex irreducible characters of finite groups. Given a finite group G,and a primep,we may consider the group algebra\(K \)G, where \(K \)is the field of fractions of a complete discrete valuation ring R of characteristic O. We assume that F = R/ir is algebraically closed of characteristic p, where 7r is the unique maximal ideal of R,and we also assume that R contains “sufficiently many” (though a finite number of) p-power roots of unity (in particular, enough to ensure that \(\mathbb{K} \) contains a splitting field for any finite group we consider in this article).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH, England

    Geoffrey R. Robinson

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  1. Geoffrey R. Robinson
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Editors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, UK

    R. W. Carter

  2. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK

    J. Saxl

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Robinson, G.R. (1998). Arithmetical Properties of Blocks. In: Carter, R.W., Saxl, J. (eds) Algebraic Groups and their Representations. NATO ASI Series, vol 517. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5308-9_11

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  • DOI: https://doi.org/10.1007/978-94-011-5308-9_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5292-1

  • Online ISBN: 978-94-011-5308-9

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