The Conway-Miyamoto correspondences for the Fischer 3-transposition groups

Abstract

In this paper, we present a general construction of 3-transposition groups as automorphism groups of vertex operator algebras. Applying to the moonshine vertex operator algebra, we establish the Conway-Miyamoto correspondences between Fischer 3-transposition groups ${\mathrm{Fi}}_{23}$ and ${\mathrm{Fi}}_{22}$ and $c=25/28$ and $c=11/12$ Virasoro vectors of subalgebras of the moonshine vertex operator algebra.

arXiv comment3 figure files (fig1.tex, fig2.tex, fig3.tex) included