Journal ArticleDOI
Exotic Fourier transform
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This article is published in Duke Mathematical Journal.The article was published on 1994-01-01. It has received 48 citations till now. The article focuses on the topics: Hartley transform & Fractional Fourier transform.read more
Citations
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Complex reflection groups, braid groups, Hecke algebras
TL;DR: Brou et al. as mentioned in this paper introduced monodromy representations of the braid groups which factorize through the Hecke algebras extending results of Cherednik Opdam Kohno and others.
Journal ArticleDOI
Finite group modular data
TL;DR: In this article, the authors identify some senses in which the finite group data is similar to, and different from, the affine data, and they also consider the data arising from a cohomological twist, explicitly in terms of quantities associated directly with the finite groups, the modular S and T matrices for a general twist, for what appears to be the first time in print.
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Modular Data: The Algebraic Combinatorics of Conformal Field Theory
TL;DR: In this paper, a self-contained introduction to conformal field theory (CFT) is given, with some background motivation and examples to give the reader a sense of the context.
Book
The Character Theory of Finite Groups of Lie Type: A Guided Tour
Meinolf Geck,Gunter Malle +1 more
TL;DR: The character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics, and has since evolved substantially as discussed by the authors, and the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne-Michel.
References
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Fusion Rules and Modular Transformations in 2D Conformal Field Theory
TL;DR: In this paper, the authors studied conformal field theories with a finite number of primary fields with respect to some chiral algebra and showed that the fusion rules are completely determined by the behavior of the characters under the modular group.
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String theory on group manifolds
Doron Gepner,Edward Witten +1 more
TL;DR: In this article, it is shown that a 1 + 1 dimensional quantum field theory which gives a realization of current algebra (for any non-abelian Lie group G) will always give rise to an integrable representation.
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The operator algebra of orbifold models
TL;DR: In this paper, the chiral properties of (orbifold) conformal field theories were analyzed by modding out by a finite symmetry group, and the fusion rules were derived by studying the modular transformation properties of one-loop characters.
Book
Characters of reductive groups over a finite field
TL;DR: In this article, a classification of complex irreducible representations of reductive groups with connected center over a finite field is presented, using etale intersection cohomology and detailed information on representations of Weyl groups.