https://encyclopediaofmath.org/wiki/Vertex_operator encyclopediaofmath Vertex operator The term "vertex operator" in mathematics refers mainly to certain operators (in a generalized sense of the term) used in physics to describe interactions of physical states at a "vertex" in string theory [a9] and its precursor, dual resonance theory; the term refers more specifically to the closely related operators used in mathematics as a powerful tool in many applications, notably, constructing certain representations of affine Kac?Moody algebras (cf. also Kac?Moody algebra) and other infinite-dimensional Lie algebras, addressing the problems of the "Monstrous Moonshine" phenomena for the Monster finite simple group, and studying soliton equations (cf. also Moonshine conjectures). The term "vertex operator" also refers, more abstractly, to any operator corresponding to an element of a vertex operator algebra or a related operator.
