Kiyokazu Nagatomo

Conformal field theories associated to regular chiral vertex operator algebras, I: Theories over the projective line

Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line with the chiral vertex operator algebra as symmetries of the theory. We appropriately generalize the argument in [TUY] so that we are able to define sheaves of conformal blocks for chiral vertex operator algebras and study them in detail. We prove the factorization theorem under the fairly general conditions for chiral vertex operator algebras and the zero-mode algebras.

Logarithmic knot invariants arising from restricted quantum groups

We construct knot invariants from the radical part of projective modules of the restricted quantum group

SOME REMARKS ON PSEUDO-TRACE FUNCTIONS FOR ORBIFOLD MODELS ASSOCIATED WITH SYMPLECTIC FERMIONS

\overline{\mathcal{U}}_{q}(sl_{2})

Moonshine: The First Quarter Century and Beyond: Quasi-finite Algebras Graded by Hamiltonian and Vertex Operator Algebras

at

Finiteness of conformal blocks over compact Riemann surfaces

q = {\rm exp}(\pi \sqrt{-1}/p)

Explicit description of ansatz En for the Ernst equation in general relativity

, and we also show a relation between these invariants and the colored Alexander invariants. These projective modules are related to logarithmic conformal field theories.

Classification of Irreducible Modules for the Vertex Operator Algebra M(1)+: II. Higher Rank☆

We give a method to construct pseudo-trace functions for vertex operator algebras satisfying Zhus finiteness condition not through higher Zhus algebras and apply our method to the Z_2-orbifold model associated with d-pairs of symplectic fermions. For d=1, we determine the dimension of the space of one-point functions. For d>1, we construct 2^{2d-1}+3 linearly independent one-point functions and study their values at the vacuum vector.

Modular Forms and Second Order Ordinary Differential Equations: Applications to Vertex Operator Algebras

A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced and various module categories over quasi-finite algebras are described. When applied to the current algebras (universal enveloping algebras) of vertex operator algebras satisfying Zhu’s C2-finiteness condition, our general consideration derives important consequences on representation theory of such vertex operator algebras. In particular, the category of modules over such a vertex operator algebra is shown to be equivalent to the category of modules over a finite-dimensional associative algebra.

A Note on Free Bosonic Vertex Algebra and Its Conformal Vectors

We study conformal blocks (the space of correlation functions) over compact Riemann surfaces associated to vertex operator algebras which are the sum of highest weight modules for the underlying Virasoro algebra. Under the fairly general condition, for instance,

Affine Vertex Operator Algebras and Modular Linear Differential Equations

C_2