Semi-Infinite Induction and Wakimoto Modules

摘要

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. The proof of main theorem (Theorem 1.4, the semi-infinite Shapiro Lemma) is based on the independence of the choice of a resolution, which follow from the machinery of semi-infinite homological algebra developed in (13). A practical outcome of our construction is a simple construction of Wakimoto modules, which were constructed by Feigin and E. Frenkel in rather roundabout terms.