On the Notion of Metaplectic Barbasch–Vogan Duality

DOI10.1093/IMRN/RNAD097arXiv2010.16089MaRDI QIDQ6182600

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Publication date: 25 January 2024

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: In analogy with the Barbasch-Vogan duality for real reductive linear groups, we introduce a duality notion useful for the representation theory of the real metaplectic groups. This is a map on the set of nilpotent orbits in a complex symplectic Lie algebra, whose range consists of the so-called metaplectic special nilpotent orbits. We relate this duality notion with the theory of primitive ideals and extend the notion of special unipotent representations to the real metaplectic groups. We also interpret the duality map in terms of double cells of Weyl group representations.

Full work available at URL: https://arxiv.org/abs/2010.16089

Mathematics Subject Classification ID

Group theory and generalizations (20-XX) Topological groups, Lie groups (22-XX)

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