Explicit Realization of Induced and Coinduced modules over Lie Superalgebras by Differential Operators

2005/09/05 by Vladimir Molotkov, Molotkov, Vladimir
Mathematics · #17B15 #17B65 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:17B15 #msc:17B65

paper · pdf · doi:10.48550/arxiv.math/0509105

32 pages, minor changes and typo corrections

arxiv created 2005/09/08 · arxiv updated 2009/12/01

Abstract

In this article are given explicit expressions for differential operators representing the action of any element of any Lie superalgebra g on a module induced or coinduced from an h-module V, where h is any subsuperalgebra of g. For the special case where g=g₊h, and g_ is a finite-dimensional subsuperalgebra of g, whose adjoint action on g is nilpotent, there is given a practical algorithm of calculation of this action. The program in C++ making the calculations for this case is also written.

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