Height~0 characters of finite groups of Lie type
نویسندگان
چکیده
منابع مشابه
Height 0 Characters of Finite Groups of Lie Type
We give a classification of irreducible characters of finite groups of Lie type of p′-degree, where p is any prime different from the defining characteristic, in terms of local data. More precisely, we give a classification in terms of data related to the normalizer of a suitable Levi subgroup, which in many cases coincides with the normalizer of a Sylow p-subgroup. The McKay conjecture asserts...
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We prove that the duality operator preserves the Frobenius–Schur indicators of characters of connected reductive groups of Lie type with connected center. This allows us to extend a result of D. Prasad which relates the Frobenius–Schur indicator of a regular real-valued character to its central character. We apply these results to compute the Frobenius–Schur indicators of certain real-valued, i...
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Example 1.2. The trivial character of G is the homomorphism 1G defined by 1G(g) = 1 for all g ∈ G. Example 1.3. Let G be cyclic of order 4 with generator γ. Since γ4 = 1, a character χ of G has χ(γ)4 = 1, so χ takes only four possible values at γ, namely 1, −1, i, or −i. Once χ(γ) is known, the value of χ elsewhere is determined by multiplicativity: χ(γj) = χ(γ)j . So we get four characters, wh...
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An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters — those induced from a linear character of some subgroup — since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the cl...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2007
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-07-00312-3