Unipotent elements of finite groups of Lie type and realization fields their complex representations

Pam Huu Tiep, A. E. Zalesskiǐ

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29 Scopus citations


Let p be a prime. This paper classifies finite connected reductive groups G in characteristic p with the property that all complex character values of G belong to an unramified above p extension of the field of rational numbers. The main application of these results is to the problem of describing the irreducible complex (or p-adic) representations of G that remain absolutely irreducible under the Brauer reduction modulo p. An efficient approach to solve this problem for p > 3 has been developed in our paper [Proc. London Math. Soc. (3) 84 (2002) 439]. Together with [Proc. London Math. Soc. (3) 84 (2002) 439], Theorem 1.9 of the paper solves this problem for many finite connected reductive groups in characteristic p > 3. Additionally, we show that all complex representations of any finite connected reductive group with no composition factor of type E7 (2f), E8 (2f), and E8 (5f) can be realized over a quadratic extension of an unramified (above p) extension of ℚ.

Original languageEnglish (US)
Pages (from-to)327-390
Number of pages64
JournalJournal of Algebra
Issue number1
StatePublished - Jan 1 2004
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory


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