Related papers: Vertex algebraic intertwining operators among gene…
Let $V$ be a strongly rational vertex operator algebra, and let $g_1, g_2, g_3$ be three commuting finitely ordered automorphisms of $V$ such that $g_1g_2=g_3$ and $g_i^T=1$ for $i=1, 2, 3$ and $T\in \N$. Suppose $M^1$ is a $g_1$-twisted…
Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…
In this paper we study the representations of loop Affine-Virasoro Algebras. As they have canonical triangular decomposition, we define Verma modules and its irreducible quotients. We give necessary and sufficient condition for an…
We describe a natural structure of an abelian intertwining algebra (in the sense of Dong and Lepowsky) on the direct sum of the untwisted vertex operator algebra constructed {}from the Leech lattice and its (unique) irreducible twisted…
Generalizing some of our earlier work, we prove natural presentations of the principal subspaces of the level one standard modules for the untwisted affine Lie algebras of types A, D and E, and also of certain related spaces. As a…
We study the general twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra $V$. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators…
The irreducible modules for the parafermion vertex operator algebra associated to any finite dimensional Lie algebra and any positive integer are identified, the quantum dimensions are computed and the fusion rules are determined.
Let $V$ be a $C_2$-cofinite vertex operator algebra without nonzero elements of negative weights. We prove the conjecture that the spaces spanned by analytic extensions of pseudo-$q$-traces ($q=e^{2\pi i\tau}$) shifted by $-\frac{c}{24}$ of…
We discuss a recent proof by the author of a general version of the Verlinde conjecture in the framework of vertex operator algebras and the application of this result to the construction of modular tensor tensor category structure on the…
We classify and explicitly construct the embedding diagrams of Verma modules over the N=2 supersymmetric extension of the Virasoro algebra. The essential ingredient of the solution consists in drawing the distinction between two different…
We study canonical intertwining operators between modules of the trigonometric Cherednik algebra, induced from the standard modules of the degenerate affine Hecke algebra. We show that these operators correspond to the Zhelobenko operators…
We initiate a new study of differential operators with symmetries and combine this with the study of branching laws for Verma modules of reductive Lie algebras. By the criterion for discretely decomposable and multiplicity-free restrictions…
After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…
Verlinde's formula for rational vertex operator algebras computes the fusion rules from the modular transformations of characters. In the non semisimple and non finite case, a logarithmic Verlinde formula has been proposed together with…
The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.
We classify and construct $SL(n,\mathbb{R})$-intertwining differential operators $\mathcal{D}$ from a line bundle to a vector bundle over the real projective space $\mathbb{RP}^{n-1}$ by the F-method. This generalizes a classical result of…
Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let S be a finite set of inequivalent irreducible V-modules which is…
We use the theory of vertex operator algebras and intertwining operators to obtain systems of q-difference equations satisfied by the graded dimensions of the principal subspaces of certain level k standard modules for \hat{\goth{sl}(3)}.…
We pursue our study of generalised Kac-Moody and Virasoro algebras defined on compact homogeneous manifolds. Extending the well-known Vertex operator in the case of the two-torus or the two-sphere, we obtain explicit bosonic realisations of…
This paper presents explicit formulas for intertwining operators of the quantum group $U_q(sl_2)$ acting on tensor products of Verma modules. We express a first set of intertwining operators (the holographic operators) in terms of the…