Abstract
The purpose of this paper is to suggest the construction and study properties of semi-infinite induction, which relates to semi-infinite cohomology the same way induction relates to homology and coinduction to cohomology. We prove a version of the Shapiro Lemma, showing that the semi-infinite cohomology of a module is isomorphic to that of the semi-infinitely induced module. A practical outcome of our construction is a simple construction of the Wakimoto modules, highest-weight modules used in double-sided BGG resolutions of irreducible modules.
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