Vertex operator algebras, the Verlinde conjecture, and modular tensor categories
YZ Huang - Proceedings of the National Academy of …, 2005 - National Acad Sciences
… Our main theorems on the Verlinde conjecture, on the Verlinde formula for the … Verlinde
conjecture is given in this section. In section 3 our main theorem on the modular tensor category …
conjecture is given in this section. In section 3 our main theorem on the modular tensor category …
From the representation theory of vertex operator algebras to modular tensor categories in conformal field theory
J Lepowsky - Proceedings of the National Academy of …, 2005 - National Acad Sciences
… the Verlinde conjecture and modular tensor category structure, … ) proof of the Verlinde
conjecture in a very general form, … of a previously constructed tensor category. This work, along …
conjecture in a very general form, … of a previously constructed tensor category. This work, along …
The Steinberg Tensor Product Theorem for General Linear Group Schemes in the Verlinde Category
AS Kannan - arXiv preprint arXiv:2404.02786, 2024 - arxiv.org
… tensor category, V ∗ denote the dual of an object V , M denote the Deligne tensor product of
two symmetric tensor categories… Then, we conjecture that any irreducible representation of G …
two symmetric tensor categories… Then, we conjecture that any irreducible representation of G …
Algebraic geometry and representation theory in the Verlinde category
SSN Venkatesh - 2019 - dspace.mit.edu
… will include definitions of symmetric tensor categories and the formal construction of the
Verlinde … In fact, for a while, it was conjectured that the above theorem held for C any symmetric …
Verlinde … In fact, for a while, it was conjectured that the above theorem held for C any symmetric …
Tensor categories for vertex operator superalgebra extensions
T Creutzig, S Kanade, R McRae - arXiv preprint arXiv:1705.05017, 2017 - arxiv.org
… tensor category structure, Huang solved the two major important problems we have mentioned
above: determination of the modularity of these categories and the Verlinde conjecture. …
above: determination of the modularity of these categories and the Verlinde conjecture. …
Logarithmic conformal field theory, log-modular tensor categories and modular forms
T Creutzig, T Gannon - Journal of Physics A: Mathematical and …, 2017 - iopscience.iop.org
… Overarching these pillars is the Verlinde formula. In this paper we … conjecture 3.3, the
semi-simplification of a log-modular tensor category is expected to be a modular tensor category…
semi-simplification of a log-modular tensor category is expected to be a modular tensor category…
Vertex operator algebras and the Verlinde conjecture
YZ Huang - Communications in Contemporary Mathematics, 2008 - World Scientific
… The results of the present paper have been used in [20] to prove the rigidity and modularity
of the tensor category of modules for a vertex operator algebra satisfying the conditions …
of the tensor category of modules for a vertex operator algebra satisfying the conditions …
Hopf algebras and finite tensor categories in conformal field theory
J Fuchs, C Schweigert - arXiv preprint arXiv:1004.3405, 2010 - arxiv.org
… We focus on generalizations of the Verlinde formula, for which … presence of a Hopf algebra
internal to finite tensor categories. … Namely, the (conjectured) tensor product of any two simple …
internal to finite tensor categories. … Namely, the (conjectured) tensor product of any two simple …
Tensor products of modules for a vertex operator algebra and vertex tensor categories
YZ Huang, J Lepowsky - Lie Theory and Geometry: In Honor of Bertram …, 1994 - Springer
… three-manifold invariants, ChernSimons theory, the Verlinde formula, etc. (see for … conjectured
in [FLM2] and proved in [Do]. It was also conjectured in [FLM2] (and it remains a conjecture…
in [FLM2] and proved in [Do]. It was also conjectured in [FLM2] (and it remains a conjecture…
Affine Lie algebras and tensor categories
YZ Huang - arXiv preprint arXiv:1811.05123, 2018 - arxiv.org
… tensor category structures on module categories for affine Lie algebras. We discuss the results
that were first conjectured in … But it was the Verlinde formula and modular tensor category …
that were first conjectured in … But it was the Verlinde formula and modular tensor category …
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