Sentence examples for irreducible character from inspiring English sources

Let φ be a non-linear irreducible character of G ′.

Let G be a finite group; L ( G ) denotes the largest irreducible character degree of G and S ( G ) denotes the second largest irreducible character degree of G.

Case 1. | G / G ′ | > p. Let φ be a non-linear irreducible character of G ′.

Therefore, only the principal character of G ′ is extendible to an irreducible character of G.

By Lemma 2.1, G ′ is abelian or has exactly one non-linear irreducible character.

Let β be a non-principle irreducible character of G ′ and φ an irreducible character of G ″ such that [ β G ″, φ ] ≠ 0. Then β G ″ = φ or β = φ G ″. Subcase 2.1.

More specifically, he is interested in wave front cycles of tempered representations, Fourier transforms of nilpotent coadjoint orbits, irreducible characters, and branching laws for discrete series.

When χ is irreducible, this formula gives us the number of times it appears in the decomposition of χʹ into irreducibles, because the irreducible characters are orthogonal with respect to this inner product.

To compute the decomposition of a character into irreducible characters, we can use the inner product on characters: 〈χ, χ'〉 = 1/|A10| ΣC|C|χ(C χ'(C), where C ranges over all the conjugacy classes of A10.

The Langlands classification and irreducible characters (with J. Adams and D. Vogan), Birkhauser (1992), Boston-Basel-Berlin. Unipotent representations for real reductive groups, Proceedings of ICM, Kyoto 1990 19900), Springer-Verlag, Math.

G has exactly three irreducible characters induced from irreducible characters of G ′. Let β = λ G, α = μ G and γ = η G be the three irreducible characters, where β, α, γ ∈ Irr ( G ) and λ, μ, η ∈ Irr ( G ′ ).