Logarithmic knot invariants arising from restricted quantum groups (2007)
Murakami, Jun, Nagatomo, Kiyokazu
We construct knot invariants from the radical part of projective modules of restricted quantum groups. We also show a relation between these invariants and the colored Alexander invariants.
Akihiro Tsuchiya, Nagatomo, Kiyokazu
Given a chiral vertex operator algebra satisfying a suitable finiteness condition with semisimplicity of the zero-mode algebra as well as a regularity condition for induced modules, we construct...
Quasi-finite algebras graded by Hamiltonian and vertex operator algebras (2005)
Matsuo, Atsushi, Nagatomo, Kiyokazu, Tsuchiya, Akihiro
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...
Nagatomo, Kiyokazu, Tsuchiya, Akihiro
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...
Finiteness of conformal blocks over compact Riemann surfaces (2002)
Abe, Toshiyuki, Nagatomo, Kiyokazu
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...
Dong, Chongying, Mason, Geoffrey, Nagatomo, Kiyokazu
We study graded traces of vectors in free bosonic vertex operator algebras and lattice vertex operator algebras. We show in particular that trace functions in these two theories always have the shape...
Dong, Chongying, Mason, Geoffrey, Nagatomo, Kiyokazu
We study graded traces of vectors in free bosonic vertex operator algebras and lattice vertex operator algebras. We show in particular that trace functions in these two theories always have the shape...
Classification of irreducible modules for the vertex operator algebra M(1)^+, II: higher rank (1999)
Dong, Chongying, Nagatomo, Kiyokazu
The vertex operator algebra M(1)^+ is the fixed point set of free bosonic vertex operator algebra M(1) under the -1 automorphism. All irreducible modules for M(1)^+ are classified in this paper for...
Automorphism Groups and Twisted Modules for Lattice Vertex Operator Algebras (1998)
Dong, Chongying, Nagatomo, Kiyokazu
We give a complete description of the full automorphism group of a lattice vertex operator algebra, determine the twisted Zhu's algebra for the automorphism lifted from the -1 isometry of the lattice...
Representations of vertex operator algebra V_L^+ for rank one lattice L (1998)
Dong, Chongying, Nagatomo, Kiyokazu
We classify the irreducible modules for the fixed point vertex operator subalgebra V_L^+ of the vertex operator algebra V_L associated to a positive definite even lattice of rank 1 under the...
Classification of irreducible modules for the vertex operator algebra M(1)^+ (1998)
Dong, Chongying, Nagatomo, Kiyokazu
We classify the irreducible modules for the fixed point vertex operator subebra of the rank 1 free bosonic VOA under the -1 automorphism.
On axioms for a vertex algebra and the locality of quantum fields (1997)
Matsuo, Atsushi, Nagatomo, Kiyokazu
The identities satisfied by two-dimensional chiral quantum fields are studied from the point of view of vertex algebras. The Cauchy-Jacobi identity (or the Borcherds identity) for three mutually...
A note on free bosonic vertex algebra and its conformal vectors (1997)
Matsuo, Atsushi, Nagatomo, Kiyokazu
We classify all the Heisenberg and conformal vectors and determine the full automorphism group of the free bosonic vertex algebra without gradation. To describe it we introduce a notion of inner...