Representations and Characters of Groups

By G. James, Martin W. Liebeck. 2001

694 citations recorded by the source corpus.

Subfields: Molecular Biology, Organic Chemistry, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/37d8e1bac21fb73e598d46677c5a8b9463bc4a2f

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Citations in the corpus

Tensor categories: a selective guided tour (2008, background): “ there are non-isomorphic ﬁnite groups with isomorphic character tables. (The simplest example is given by the dihedral group D8 = Z4 ⋊Z2 and the quaternion group Q, cf. any elementary textbook, e.g. [123].) Since D8 and Qhave the same number of irreducible representations, the categories RepD8 and ”
The q, t-Catalan numbers and the space of diagonal harmonics : with an appendix on the combinatorics of Macdonald polynomials (2007, background): “Maschke’s theorem [JL01] says that every V can be expressed as a direct sum of irreducible submodules.”
Finite-dimensional pointed Hopf algebras with alternating groups are trivial (2008, neutral): “σ and [S σ : A σ] = 2 (see for instance [ JL , Proposition 12.17]).”
Representation theory for high-rate multiple-antenna code design (2001, background): “Hence, irreducible fixed-point-free representations of cyclic groups are exactly the primitive characters of the group, and these are characters that map a generator of the group to a primitive th root of unity.”
An introduction to multivariate Krawtchouk polynomials and their applications (2013, background): “rGroups. Let G be a ﬁnite group with conjugacy classes C 1,C 2,...,Cd and irreducible characters χ 1,...,χd. Label those so that Cd = {id}, χ 1 ≡ 1 (the trivial character). Background can be found in James and Liebeck (2001), Issacs (1994), Diaconis (1988). Deﬁne pi = |Ci|/|G|, for i = 1,...,d. It i”
Arithmetic quotients of the mapping class group (2013, background): “16 from [19] with some mild modification.”
Tight Frames and Their Symmetries (2004, methodology): “Fourier analysis on abelian groups, e.g., [ JL93 ] and [Ru62] . LetG be a finite abelian group.”