Representation groups of characters
نویسندگان
چکیده
منابع مشابه
Characters of Nonlinear Groups
Two of the primary methods of constructing automorphic forms are the Langlands program and Howe's theory of dual pairs. The Langlands program concerns a reductive linear group G deened over a number eld. Associated to G is its dual group L G. The con-jectural principle of functoriality says that a homomorphism L H ! L G should provide a \transfer" of automorphic representations from H to those ...
متن کاملCharacters of Finite Abelian Groups
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...
متن کاملOn characters of Weyl groups
In this note a combinatorial character formula related to the symmetric group is generalized to an arbitrary finite Weyl group. 1 The Case of the Symmetric Group The length l(π) of a permutation π ∈ Sn is the number of inversions of π, i.e., the number of pairs (i, j) with 1 ≤ i < j ≤ n and π(i) > π(j). For any permutation π ∈ Sn let m(π) be defined as (1) m(π) :=
متن کاملCharacters of Finite Abelian Groups
When G has size n and g ∈ G, for any character χ of G we have χ(g)n = χ(gn) = χ(1) = 1, so the values of χ lie among the nth roots of unity in S1. More precisely, the order of χ(g) divides the order of g (which divides #G). Characters on finite abelian groups were first studied in number theory, since number theory is a source of many interesting finite abelian groups. For instance, Dirichlet u...
متن کاملMonomial Characters of Finite Groups
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: Journal of Algebra
سال: 1986
ISSN: 0021-8693
DOI: 10.1016/0021-8693(86)90170-5