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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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}} …

Various monoidal categories, including suitable representation categories of vertex operator
algebras, admit natural Grothendieck-Verdier duality structures. We recall that such a …