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- Title
Ghost Distributions on Supersymmetric Spaces II: Basic Classical Superalgebras.
- Authors
Sherman, Alexander
- Abstract
We study ghost distributions on supersymmetric spaces for the case of basic classical Lie superalgebras. We introduce the notion of interlaced pairs, which are those for which both |$({\mathfrak{g}},{\mathfrak{k}})$| and |$({\mathfrak{g}},{\mathfrak{k}}^{\prime})$| admit Iwasawa decompositions. For such pairs, we define a ghost algebra, generalizing the subalgebra of |${\mathcal{U}}{\mathfrak{g}}$| defined by Gorelik. We realize this algebra as an algebra of |$G$| -equivariant operators on the supersymmetric space itself, and for certain pairs, the "special" ones, we realize our operators as twisted-equivariant differential operators on |$G/K$|. We additionally show that the Harish-Chandra morphism is injective, compute its image for all rank one pairs, and provide a conjecture for the image when |$({\mathfrak{g}},{\mathfrak{k}})$| is interlaced.
- Subjects
SUPERALGEBRAS; DIFFERENTIAL operators; ALGEBRA; LIE superalgebras; INJECTIVE functions; MORPHISMS (Mathematics)
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 5, p3706
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad089