Groups with a Steinberg character
نویسندگان
چکیده
منابع مشابه
Corrigendum to “the Weil-steinberg Character of Finite Classical Groups”
This paper corrects the statement and the proof of Theorem 1.5 of the paper quoted in the title (Represent. Theory 13 (2009), 427–459). Theorem 1.5 of our paper [1] requires a correction. Below we provide a new statement of this theorem and correct the proof. A mistake in the original proof of Theorem 1.5 is due to missing the multiple 2 at a certain point of the proof (see [1, page 456, line 2...
متن کاملTensoring Generalized Characters with the Steinberg Character
Let G be a reductive connected algebraic group over an algebraic closure of a finite field of characteristic p. Let F be a Frobenius endomorphism on G and write G := G F for the corresponding finite group of Lie type. We consider projective characters of G in characteristic p of the form St ·β, where β is an irreducible Brauer character and St the Steinberg character of G. Let M be a rational G...
متن کاملSteinberg groups as amalgams
For any root system and any commutative ring, we give a relatively simple presentation of a group related to its Steinberg group St. This includes the case of infinite root systems used in Kac–Moody theory, for which the Steinberg group was defined by Tits and Morita–Rehmann. In most cases, our group equals St, giving a presentation with many advantages over the usual presentation of St. This e...
متن کاملPrincipal Blocks and the Steinberg Character
We determine the finite simple groups of Lie type of characteristic p, for which the Steinberg character lies in the principal `-block for every prime ` 6= p dividing the order of the group. In [1, Corollary 4.4], Bessenrodt, Malle, and Olsson determine the finite simple groups of Lie type having a non-trivial irreducible character which is in the principal `-block for all primes ` dividing the...
متن کاملOn the Steinberg character of a semisimple p-adic group
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 1972
ISSN: 0025-5874,1432-1823
DOI: 10.1007/bf01111569