# Technique in computing the characters of VOA modules using vector-valued functions for modular groups

## Keywords:

vector-valued functions, vertex operator algebra(VOA), Modular tensor category(MTC)## Abstract

For a rational vertex operator algebra (VOA) with a -graded simple -module , there is a corresponding character

where is the subspace of on which acts by multiplication by , is the central charge of and .

In this paper, we apply the notion of vector-valued functions for a modular group from the work of Peter Bantay and Terry Gannon to compute the -module character . With the relation among simple -modules and their corresponding simple objects of modular tensor category (MTC) , we can use the central charge and conformal weights of the MTC to compute the character . This technique can be used to compute up to central charge by the restriction mentioned in P. Bantay paper.