Linear representations of finite groups

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General E(2)-Equivariant Steerable CNNs (2019, methodology): “A decomposition can be found by exploiting basic results of character theory and linear algebra [29].”
Linear Representations of the Automorphism Group of a Free Group (2006, background): “-modules. Clearly the left hand side of (52) is contained in the right hand side. Note that, since His normal in Gthe module Qis also induced from any of the Q0,...,Qr. The Frobenius reciprocity law ([32], chapter 7) implies that none of the Q0,...,Qr can occur as an irreducible constituent of the r”
Twisting Commutative Algebraic Groups (2006, background): “The irreducible rational representations of G are in one-to-one correspondence with the cyclic extensions of k in L. (See for example exercise 13.1 of [ Se2 ].) Namely, if ρ is an irreducible rational representation let Fρ be the fixed field of the kernel of ρ, and if F is a cyclic extension of k in”
Some groups of type VF (2003, background): “The Artin induction theorem for kP-modules ([58], 9.”
Representation and character theory in 2-categories (2006, background): “is a class function. The following is well known [ Ser77 ].”
Group theoretical methods in machine learning (2008, background): “In fact, the complete set of irreducible characters forms an orthogonal basis for the space of class functions [Serre, 1977, Theorem 6].”