Linear Representations of Finite Groups

By Randall R. Holmes. 2008

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Citations in the corpus

Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network (2018, background): “From a mathematical point of view, the relevance of Fourier theoretic ideas in all these cases is a direct consequence of equivariance, specifically, of the fact that the {T s g }g∈G operators form a representation of the underlying group, in the algebraic sense of the word [20].”
N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials (2018, background): “For more background in representation theory, the reader is referred to (Serre, 1977).”
Twisted Burnside-Frobenius theory for discrete groups (2006, unknown): “In the formulation of key technical Theorem 3.10, item (1) in [1] the words “f.g.” (finitely generated) are missed.”
Formulation of lattice gauge theories for quantum simulations (2014, background): “Note that ∑ J dim (J) Tr ( DJ ( g−1h )) is the character of the regular representation of g−1h, which is equal to |G| if g−1h = 1 and vanishes otherwise [55].”
Linear Representations of the Automorphism Group of a Free Group (2006, background): “Now Proposition 24 of [32] says that Q is either isotypic or induced.”
Introduction to representation theory (2009, unknown): “For a more detailed treatment of these topics, we refer the reader to the textbooks [S], [FH], and [CR].”
Finite part of operator K-theory for groups finitely embeddable into Hilbert space and the degree of non-rigidity of manifolds (2013, background): “We remark that rationally all representations of finite groups are induced from finite cyclic groups; see Serre [26].”
Family of non-Abelian Kitaev models on a lattice: Topological condensation and confinement (2007, background): “Given a finite group G and a normal subgroup H ⊂ G, let (H,G)cj be the set of conjugacy classes of G contained in H and (H,G)ir be the set of induced representations in G of irreducible representations in H , up to isomorphisms[63].”
Good reduction of abelian varieties (2014, background): “See [37] for a proof of this fact.”
Unit Interval Orders and the Dot Action on the Cohomology of Regular Semisimple Hessenberg Varieties (2015, unknown): “The term variety by itself will still refer to an integral, separated scheme of ﬁnite type over an algebraically closed ﬁeld”