Tensor decomposition, parafermions, level-rank duality, and reciprocity law for vertex operator algebras
Z Lin - arXiv preprint arXiv:1406.4191, 2014 - arxiv.org
For the semisimple Lie algebra $\frak {sl} _n $, the basic representation $ L_ {\widehat {\frak
{sl} _ {n}}}(1, 0) $ of the affine Lie algebra $\widehat {\frak {sl} _ {n}} $ is a lattice vertex …
{sl} _ {n}}}(1, 0) $ of the affine Lie algebra $\widehat {\frak {sl} _ {n}} $ is a lattice vertex …
A theory of tensor products for vertex operator algebra satsifying C_2-cofiniteness
M Miyamoto - arXiv preprint math/0309350, 2003 - arxiv.org
We reformed the tensor product theory of vertex operator algebras developed by Huang and
Lepowsky so that we could apply it to all vertex operator algebras satisfying C_2 …
Lepowsky so that we could apply it to all vertex operator algebras satisfying C_2 …
[HTML][HTML] Logarithmic link invariants of U‾ qH (sl2) and asymptotic dimensions of singlet vertex algebras
T Creutzig, A Milas, M Rupert - Journal of Pure and Applied Algebra, 2018 - Elsevier
We study relationships between the restricted unrolled quantum group U‾ q H (sl 2) at q= e π
i/r, and the singlet vertex operator algebra M (r), r≥ 2. We use deformable families of …
i/r, and the singlet vertex operator algebra M (r), r≥ 2. We use deformable families of …
Ribbon tensor structure on the full representation categories of the singlet vertex algebras
T Creutzig, R McRae, J Yang - Advances in Mathematics, 2023 - Elsevier
We show that the category of finite-length generalized modules for the singlet vertex algebra
M (p), p∈ Z> 1, is equal to the category OM (p) of C 1-cofinite M (p)-modules, and that this …
M (p), p∈ Z> 1, is equal to the category OM (p) of C 1-cofinite M (p)-modules, and that this …
Representation theory of 𝐿_ {𝑘}(𝔬𝔰𝔭 (1| 2)) from vertex tensor categories and Jacobi forms
T Creutzig, J Frohlich, S Kanade - Proceedings of the American …, 2018 - ams.org
Representation theory of 𝐿_{𝑘}(𝔬𝔰𝔭(1\vert2)) from vertex tensor categories and Jacobi forms
Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 146, Number …
Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 146, Number …
On ribbon categories for singlet vertex algebras
T Creutzig, R McRae, J Yang - Communications in Mathematical Physics, 2021 - Springer
We construct two non-semisimple braided ribbon tensor categories of modules for each
singlet vertex operator algebra M (p), p≥ 2. The first category consists of all finite-length M …
singlet vertex operator algebra M (p), p≥ 2. The first category consists of all finite-length M …
Tensor category KLk (sl2n) via minimal affine W-algebras at the non-admissible level k=− 2n+ 12
We prove that the Kazhdan-Lusztig category of sl ˆ m at level k, KL k (sl m), is a semi-simple,
rigid braided tensor category for all even m≥ 4, and k=− m+ 1 2. Moreover, all modules in …
rigid braided tensor category for all even m≥ 4, and k=− m+ 1 2. Moreover, all modules in …
Tensor categories and the mathematics of rational and logarithmic conformal field theory
YZ Huang, J Lepowsky - Journal of Physics A: Mathematical and …, 2013 - iopscience.iop.org
We review the construction of braided tensor categories and modular tensor categories from
representations of vertex operator algebras, which correspond to chiral algebras in physics …
representations of vertex operator algebras, which correspond to chiral algebras in physics …
Level-rank duality for vertex operator algebras of types B and D
C Jiang, CH Lam - arXiv preprint arXiv:1703.04889, 2017 - arxiv.org
For the simple Lie algebra $\frak {so} _m $, we study the commutant vertex operator algebra
of $ L_ {\hat {\frak {so}} _ {m}}(n, 0) $ in the $ n $-fold tensor product $ L_ {\hat {\frak {so}} …
of $ L_ {\hat {\frak {so}} _ {m}}(n, 0) $ in the $ n $-fold tensor product $ L_ {\hat {\frak {so}} …
Grothendieck-Verdier duality in categories of bimodules and weak module functors
J Fuchs, G Schaumann, C Schweigert… - arXiv preprint arXiv …, 2023 - arxiv.org
Various monoidal categories, including suitable representation categories of vertex operator
algebras, admit natural Grothendieck-Verdier duality structures. We recall that such a …
algebras, admit natural Grothendieck-Verdier duality structures. We recall that such a …