arXiv subjects
Publications and source records attributed to Masahiko Miyamoto.
We determined the inner products of two conformal vectors with central charge 1/2 whose τ-involutions generates S_3 if none of τ-involutions are trivial. We also see that a subVA generated by such conformal vectors is a VOA with central charge 1/2+20/21 or $4/5+6/7 and has a Griess algebra of dimension three or four, respectively.
We extend the modular invariance property of the trace functions of vertex operator algebra on the set of irreducible modules (Zhu's theory) to the case of trace functions of intertwining operators.
We introduce theta-functions of VOA-modules and show that the space spanned by them has a modular invariance property.
We give a new construction of the moonshine VOA V^{\natural} over the real number field. We proved that V^{\natural} has a positive definite invariant bilinear form and its full automorphism group is the Monster simple group. We also construct an infinite series of meromorphic VOAs whose full automorphism groups are finite. We calculate the trace form on V^{\natural} for some element of the Monster.
We define an automorphism of VOA of order 3 by using a sub VOA isomorphic to a direct sum of 3-state Potts models $L(\ff,0)$ and an its module $L(\ff,3)$. This automorphism is a 3A element of the monster simple group if $V$ is the moonshine VOA $V^{\natural}$.
We prove the Galois correspondence between the subgroups of a finite automorphism group G of a simple vertex operator algebra V and the vertex operator subalgebras of V containing the set V^G of G-invariants.
We study a vertex operator algebra containing a tensor product of Ising models. It is a direct sum of code vertex operator algebra and its irreducible modules. Therefore, we classify all irreducible modules of code vertex operator algebras and show a new construction of vertex operator algebras.