Topological Frobenius reciprocity and invariant Hermitian forms
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Publication:6351609
arXiv2010.09120MaRDI QIDQ6351609
Publication date: 18 October 2020
Abstract: In his article "Unitary Representations and Complex Analysis", David Vogan gives a characterization of the continuous invariant Hermitian forms defined on the compactly supported sheaf cohomology groups of certain homogeneous analytic sheaves defined on open orbits in generalized flag manifolds. In the last section of the manuscript, Vogan raises a question about the possibility of a topological Frobenius reciprocity for these representations. In this article we give a specific version of the topological reciprocity in the regular, antidominant case and use it to study the existence of continuous invariant hermitian forms on the sheaf cohomology. In particular, we obtain a natural relationship between invariant forms on the sheaf cohomology and invariant forms on the geometric fiber.
Group actions on varieties or schemes (quotients) (14L30) Grassmannians, Schubert varieties, flag manifolds (14M15) Semisimple Lie groups and their representations (22E46) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)
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