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, 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, W3 algebra at c=4/5 or W4 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.
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