On the notion of metaplectic Barbasch-Vogan duality
arXiv:2010.16089 · doi:10.1093/imrn/rnad097
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.
arXiv commentTo appear in Int. Math. Res. Not. IMRN, rnad097
References in corpus (5)
- Invariants and K-spectrums of local theta lifts
- Endoscopy for Hecke categories, character sheaves and representations
- Whittaker unitary dual of affine graded Hecke algebras of type E
- Special unipotent representations of real classical groups: counting and reduction
- Special unipotent representations of real classical groups: construction and unitarity