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The Irreducible Brauer Characters of the Finite Special Linear Groups in Non-describing Characteristics

✍ Scribed by Jochen Gruber

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 357 KB
Volume: 215
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7736

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✦ Synopsis

The irreducible Brauer characters of SL q are investigated for primes l not n Ž . dividing q. They are described in terms of a set of ordinary characters of SL q n whose reductions modulo l are a generating set of the additive group of generalized Brauer characters and the decomposition numbers of this set. These decomposition numbers are described by combinatorial means in terms of the decomposi-Ž . tion numbers of GL q . The latter have been investigated in great detail the last n 15 years and are known completely for n F 10. ᮊ 1999 Academic Press * This paper is a contribution to the DFG project ''Algorithmic Number Theory and Algebra.'' The author gratefully acknowledges financial support from the DFG and thanks the University of Illinois at Chicago for hospitality during a part of the time when writing this article.

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