TY - JOUR
T1 - Semi-infinite induction and Wakimoto modules
AU - Voronov, Alexander A.
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 1999/10
Y1 - 1999/10
N2 - 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.
AB - 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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U2 - 10.1353/ajm.1999.0037
DO - 10.1353/ajm.1999.0037
M3 - Article
AN - SCOPUS:0033211931
VL - 121
SP - 1079
EP - 1094
JO - American Journal of Mathematics
JF - American Journal of Mathematics
SN - 0002-9327
IS - 5
ER -