Cuspidal characters and automorphisms
نویسندگان
چکیده
منابع مشابه
Endoscopic Decomposition of Characters of Certain Cuspidal Representations
We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.
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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...
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Assume G is a finite symplectic group Sp2n(q) over a finite field Fq of odd characteristic. We describe the action of the automorphism group Aut(G) on the set Irr(G) of ordinary irreducible characters of G. This description relies on the equivariance of Deligne–Lusztig induction with respect to automorphisms. We state a version of this equivariance which gives a precise way to compute the autom...
متن کاملAutomorphisms of the Fricke Characters of Free Groups
In this note, we embed the set of all Fricke characters of a free group Fn – the set of all characters of representations of Fn into SL(C) – as an irreducible affine variety VFn ∈ C 2n−1. Using the Horowitz generating set as the indeterminates, we show that the ideal In of all polynomials in these indeterminates which vanish on VFn is generated by the Magnus relation for arbitrary octets of ele...
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.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2017
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.09.026