Unipotent elements of finite groups of Lie type and realization fields of their complex representations
By Pham Huu Tiep, A. Zalesskii. 2004
48 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4b0ac48becdfe42bee7e45b6bb8a96c2acdb3318
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In Discrete Mathematics and Combinatorics
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Citations in the corpus
- Representations of finite groups of Lie type (2008, unknown): “in finite classical groups (see more on [8], [19], and [71]).”
- Real conjugacy classes in algebraic groups and finite groups of Lie type (2005, background): “3 is easy and known to experts, while the unipotent case has been essentially solved in [19]:”