Mod p Reducibility of Unramified Representations of Finite Groups of Lie Type.

Autor:	Tiep, Pham Huu, Zalesskii, A. E.
Předmět:	FINITE groups FC-groups GROUP theory COLLEGE teachers TEACHERS
Zdroj:	Proceedings of the London Mathematical Society; 2002, Vol. 84 Issue 2, p439-472, 34p
Abstrakt:	Dedicated to the memory of Professor A. I. KostrikinThe main problem under discussion is to determine, for quasi-simple groups of Lie type G, irreducible representations φ of G that remain irreducible under reduction modulo the natural prime p. The method is new. It works only for p >3 and for representations φ that can be realized over an unramified extension of Qp, the field of p -adic numbers. Under these assumptions, the main result says that the trivial and the Steinberg representations of G are the only representations in question provided G is not of type A1. This is not true for G=SL(2, p). The paper contains a result of independent interest on infinitesimally irrreducible representations ρ of G over an algebraically closed field of characteristic p. Assuming that G is not of rank 1 and G≠ G2(5), it is proved that either the Jordan normal form of a root element contains a block of size d with 1
Databáze:	Complementary Index
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