Norton's Trace Formulae for the Griess Algebra of a Vertex Operator Algebra 
with Larger Symmetry 
Atsushi Matsuo 

Abstract: Formulae expressing the trace of the composition of several (up to 
five) adjoint actions of elements of the Griess algebra of a vertex operator 
algebra are derived under certain assumptions on the action of the 
automorphism group. They coincide, when applied to the moonshine module 
$V^\natural$, with the trace formulae obtained in a different way by S.Norton, 
and the spectrum of idempotents related to 2A, 2B, 3A and 4A element of the 
Monster is determined by the representation theory of Virasoro algebra at 
$c=1/2$, $W_3$ algebra at $c=4/5$ or $W_4$ algebra at $c=1$. The 
generalization to the trace function on the whole space is also given for the 
composition of two adjoint actions, which can be used to compute the 
McKay-Thompson series for a 2A involution of the Monster. 

Math Subject Class: 17B69 (Primary) 20D08, 81R10 (Secondary)