Induced Modules for Affine Lie Algebras

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dc.creatorFutorny, Vyacheslav
dc.creatorKashuba, Iryna
dc.date2008-10-20
dc.date2009-03-04
dc.date.accessioned2026-07-07T12:48:25Z
dc.date.available2026-07-07T12:48:25Z
dc.descriptionWe study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra ${\mathcal P}$ of an affine Lie algebra ${\mathfrak G}$, our main result establishes the equivalence between a certain category of ${\mathcal P}$-induced ${\mathfrak G}$-modules and the category of weight ${\mathcal P}$-modules with injective action of the central element of ${\mathfrak G}$. In particular, the induction functor preserves irreducible modules. If ${\mathcal P}$ is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra ${\mathcal P}^{ps}$, ${\mathcal P}\subset {\mathcal P}^{ps}$. The structure of ${\mathcal P}$-induced modules in this case is fully determined by the structure of ${\mathcal P}^{ps}$-induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. König, V. Mazorchuk [Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294] and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63].
dc.identifierhttps://arxiv.org/abs/0810.3458
dc.identifierhttp://arxiv.org/abs/0810.3458
dc.identifierSIGMA 5 (2009), 026, 14 pages
dc.identifierdoi:10.3842/SIGMA.2009.026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222046
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject17B65; 17B67
dc.titleInduced Modules for Affine Lie Algebras
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