Lie conformal superalgebras and duality of modules over linearly compact Lie superalgebras

Abstract

We construct a duality functor on the category of continuous representations of linearly compact Lie superalgebras, using representation theory of Lie conformal superalgebras. We compute the dual representations of the generalized Verma modules.

arXiv comment36 pages

References in corpus (8)

• Theory of Finite Pseudoalgebras
• Finite conformal modules over the N=2,3,4 superconformal algebras
• Representations of simple finite Lie conformal superalgebras of type W and S
• Classification of finite irreducible modules over the Lie conformal superalgebra CK6
• Irreducible modules over finite simple Lie conformal superalgebras of type K
• Representations of the Exceptional Lie superalgebra $E(3,6): II. Four series of degenerate modules
• Finite irreducible conformal modules over the Lie conformal superalgebra $\mathcal{S}(p)$
• Morphisms of Verma modules over exceptional Lie superalgebra E(5,10)

Cited by in corpus (4)

• Classification of degenerate Verma modules for E(5,10)
• Classification of finite irreducible conformal modules for $K_4^{\prime }$
• An upper bound on the degree of singular vectors for $E(1,6)$
• Computation of the homology of the complexes of finite Verma modules for $K_4^{\prime }$