Abstract
The representation theory of infinite-dimensional groups is an important tool for studying conformal field theory, problems in statistical mechanics, and string theory. Using the ideas of classical representation theory and basic facts of functional analysis, the author of this monograph constructs the spin representations of the infinitesimal orthogonal group and the metaplectic representation of an infinite-dimensional symplectic group. A constructive approach is chosen. The author discusses loop algebras and the Virasoro algebra and gives applications in the last chapter.
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