具有较大对称性的顶点算子代数的Griess代数的Norton迹公式
Norton's Trace Formulae for the Griess Algebra of a Vertex Operator Algebra with Larger Symmetry
摘要：
在对自同构群作用的某些假设下，导出了表示顶点算子代数的Griess代数的元素的几个（最多五个）伴随作用的合成迹的公式.当应用于月光模块$V^\natural$时，它们与S.Norton以不同的方式获得的迹公式一致，并且与Monster的2A，2B，3A和4A元素相关的幂等元的谱由$c=1/2$的Virasoro代数，$c=4/5$的$W_3$代数或$c=1$的$W_4$代数的表示论确定。对于两个伴随作用的合成，给出了全空间上迹函数的推广，可用于计算Monster的2A对合的McKay-Thompson级数.
英文摘要：
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.
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