Related papers: Rigidity and modularity of vertex tensor categorie…

For the affine vertex algebra $V_k(\mathfrak{g})$ at an admissible level $k$ of $\hat{\mathfrak{g}}$, we prove that certain subcategory of weak $V_k(\mathfrak{g})$-module category is semisimple. As a consequence, we show that…

The following integrability theorem for vertex operator algebras V satisfying some finiteness conditions(C_2-cofinite and CFT-type) is proved: the vertex operator subalgebra generated by a simple Lie subalgebra {\frak g} of the weight one…

Over a field of characteristic $p>0$, the higher Verlinde categories $\mathrm{Ver}_{p^n}$ are obtained by taking the abelian envelope of quotients of the category of tilting modules for the algebraic group $\mathrm{SL}_2$. These symmetric…

For a vertex operator algebra $V$, one may naturally define spaces of conformal blocks following a construction of Frenkel-Ben-Zvi generalized by Damiolini-Gibney-Tarasca. If $V$ is strongly rational, these spaces of conformal blocks form…

We study semi-strict tricategories in which the only weakness is in vertical composition. We construct these as categories enriched in the category of bicategories with strict functors, with respect to the cartesian monoidal structure. As…

It is shown that the support of an irreducible weight module over the Schr\"{o}dinger-Virasoro Lie algebra with an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module…

In [arXiv:1509.02937], the notion of a module tensor category was introduced as a braided monoidal central functor $F\colon \mathcal{V}\longrightarrow \mathcal{T}$ from a braided monoidal category $\mathcal{V}$ to a monoidal category…

For a simple module $M$ over the positive part of the Virasoro algebra (actually for any simple module over some finite dimensional solvable Lie algebras $\mathfrak{a}_r$) and any $\alpha\in\C$, a class of weight modules $\mathcal {N}(M,…

Let $G$ be a unimodular locally compact group. We define a property of irreducible unitary $G$-representations $V$ which we call c-temperedness, and which for the trivial $V$ boils down to F{\o}lner's condition (equivalent to the trivial…

Let $L(-{1/2}(l+1),0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{l}^{(1)}$ with the lowest admissible half-integer level $-{1/2}(l+1)$, for even l. We study the category of weak modules for that…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

In this work, we establish certain enrichments of dual algebraic structures in the setting of monoidal double categories. In more detail, we obtain a tensored and cotensored enrichment of monads in comonads, as well as a tensored and…

This paper introduces the concept of distorted monoidal categories, a generalization of monoidal and braided monoidal categories that supports non-reversible and direction-sensitive tensor structures. Unlike the classical setting, where the…

We introduce the notion of (nondegenerate) strong-modular fusion algebras. Here strongly-modular means that the fusion algebra is induced via Verlinde's formula by a representation of the modular group SL(2,Z) whose kernel contains a…

We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a general procedure which associates to every strongly local…

In this paper, we study the tensor products of irreducible highest weight modules with irreducible loop modules over the affine-Virasoro algebra with aid of the ``shifting technique" established for the Virasoro algebra in [H. Chen, X. Guo,…

It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\cal O$, or (iii) a module in Category ${\cal O}^-$, or (iv) a module which contains…

We investigate objects in symmetric tensor categories that have simultaneously finite symmetric and finite exterior algebra. This forces the characteristic of the base field to be $p>0$, and the maximal degree of non-vanishing symmetric and…

For a vertex operator algebra $V$ and a vertex operator subalgebra $V'$ which is invarinant under an automorphism $g$ of $V$ of finite order, we introduce a $g$-twisted induction functor from the category of $g$-twisted $V'$-modules to the…

The moduli space $\mathcal M(r,n)$ of framed torsion free sheaves on the projective plane with rank $r$ and second Chern class equal to $n$ has the natural action of the $(r+2)$-dimensional torus. In this paper, we look at the fixed point…