Titlebook: Linear Representations of Finite Groups; Jean-Pierre Serre Textbook 1977 Springer Science+Business Media New York 1977 Darstellung (Math.

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Generalities on linear representations linear mapping of V into V which has an inverse a.; this inverse is linear. When V has a finite basis (.) of n elements, each linear map .: V → V is defined by a square matrix (.) of order .. The coefficients . are complex numbers; they are obtained by expressing the images .(.) in terms of the basis (.):

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Artin’s theoremombination of the .’s with non-negative integer coefficients. We will denote by R. (G) the set of these functions, and by R(G) the group generated by R.(G), i.e., the set of differences of two characters. We have

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Rationality questions: examplesbers, and let .(.) be the field obtained by adjoining the .th roots of unity to .. The Galois group of .(.) over . is the group denoted Γ. in 12.4; it is a subgroup of the group (./.)*. In fact:. (Gauss). . Γ. = (./m.)*.

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https://doi.org/10.1007/978-1-4684-9458-7Darstellung (Math; ); Endliche Gruppe; Finite; algebra; character theory; mathematics; proof; theorem

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