RIGIDITY AND MODULARITY OF VERTEX TENSOR CATEGORIES

@article{Huang2005RIGIDITYAM,
  title={RIGIDITY AND MODULARITY OF VERTEX TENSOR CATEGORIES},
  author={Yi-Zhi Huang},
  journal={Communications in Contemporary Mathematics},
  year={2005},
  volume={10},
  pages={871-911}
}
  • Yi-Zhi Huang
  • Published 25 February 2005
  • Mathematics
  • Communications in Contemporary Mathematics
Let V be a simple vertex operator algebra satisfying the following conditions: (i) V(n) = 0 for n < 0, V(0) = ℂ1 and V′ is isomorphic to V as a V-module. (ii) Every ℕ-gradable weak V-module is completely reducible. (iii) V is C2-cofinite. (In the presence of Condition (i), Conditions (ii) and (iii) are equivalent to a single condition, namely, that every weak V-module is completely reducible.) Using the results obtained by the author in the formulation and proof of the general version of the… 
Vertex operator algebras, the Verlinde conjecture, and modular tensor categories.
  • Yi-Zhi Huang
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 2005
TLDR
A proof of the Verlinde conjecture for V is announced of the statement that the matrices formed by the fusion rules among irreducible V-modules are diagonalized by the matrix given by the action of the modular transformation tau |--> -1/tau on the space of characters of irreducing V- modules.
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Suppose V G is the fixed-point vertex operator subalgebra of a compact group G acting on a simple abelian intertwining algebra V . We show that if all irreducible V -modules contained in V live in
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Let V be a simple, rational, C2-cofinite vertex operator algebra and G a finite group acting faithfully on V as automorphisms, which is simply called a rational vertex operator algebra with a
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Gluing vertex algebras
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Vertex operator algebras, the Verlinde conjecture, and modular tensor categories.
  • Yi-Zhi Huang
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 2005
TLDR
A proof of the Verlinde conjecture for V is announced of the statement that the matrices formed by the fusion rules among irreducible V-modules are diagonalized by the matrix given by the action of the modular transformation tau |--> -1/tau on the space of characters of irreducing V- modules.
VERTEX OPERATOR ALGEBRAS AND THE VERLINDE CONJECTURE
We prove the Verlinde conjecture in the following general form: Let V be a simple vertex operator algebra satisfying the following conditions: (i) V(n) = 0 for n < 0, V(0) = ℂ1 and V′ is isomorphic
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TLDR
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Virasoro vertex operator algebras, the (nonmeromorphic) operator product expansion and the tensor product theory
Abstract A theory of tensor products of modules for a vertex operator algebra is being developed by Lepowsky and the author. To use this theory, one first has to verify that the vertex operator
Tensor structures arising from affine Lie algebras. III
This paper is a part of the series [KL]; however, it can be read independently of the first two parts. In [D3], Drinfeld proved the existence of an equivalence between a tensor category of
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