منابع مشابه
On the Schur indices of cuspidal unipotent characters
In previous work of Gow, Ohmori, Lusztig and the author, the Schur indices of all unipotent characters of finite groups of Lie type have been explicitly determined except for six cases in groups of type F4, E7 and E8. In this paper, we show that the Schur indices of all cuspidal unipotent characters for type F4 and E8 are 1, assuming that the group is defined over a field of “good” characterist...
متن کاملTHE SCHUR INDICES OF THE CUSPIDAL UNIPOTENT CHARACTERS OF THE FINITE CHEVALLEY GROUPS E7(q)
We show that the two cuspidal unipotent characters of a finite Chevalley group E7(q) have Schur index 2, provided that q is an even power of a (sufficiently large) prime number p such that p ≡ 1 mod 4. The proof uses a refinement of Kawanaka’s generalized Gelfand–Graev representations and some explicit computations with the CHEVIE computer algebra system.
متن کاملCharacters of unipotent groups over finite fields
Let G be a connected unipotent group over a finite field Fq. In this article we propose a definition of L-packets of complex irreducible representations of the finite group G(Fq) and give an explicit description of L-packets in terms of the so-called “admissible pairs” for G. We then apply our results to show that if the centralizer of every geometric point of G is connected, then the dimension...
متن کاملOn Degrees of Irreducible Brauer Characters
Based on a large amount of examples, which we have checked so far, we conjecture that |G|p′ ≤ ∑ φ φ(1) 2 where p is a prime and the sum runs through the set of irreducible Brauer characters in characteristic p of the finite group G. We prove the conjecture simultaneously for p-solvable groups and groups of Lie type in the defining characteristic. In non-defining characteristics we give asymptot...
متن کاملA Note on Lifting Brauer Characters
A Brauer character of a finite group may be lifted to an ordinary character if it lies in a block whose defect groups are contained in a normal p-solvable subgroup. By the Fong-Swan theorem [2, Theorem 72.1], an irreducible Brauer character of a finite p-solvable group G may be lifted to an ordinary (complex) character of G. In other words, every Brauer character is the restriction of some ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1994
ISSN: 0021-8693
DOI: 10.1006/jabr.1994.1226