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Radon transforms for quasi-equivariant D-modules on generalized flag manifolds

✍ Scribed by Corrado Marastoni; Toshiyuki Tanisaki

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 257 KB
Volume: 18
Category: Article
ISSN: 0926-2245
DOI: 10.1016/s0926-2245(02)00145-6

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✦ Synopsis

In this paper we deal with Radon transforms for generalized flag manifolds in the framework of quasi-equivariant D-modules. We shall follow the method employed by Baston-Eastwood and analyze the Radon transform using the Bernstein-Gelfand-Gelfand resolution and the Borel-Weil-Bott theorem. We shall determine the transform completely on the level of the Grothendieck groups. Moreover, we point out a vanishing criterion and give a sufficient condition in order that a D-module associated to an equivariant locally free O-module is transformed into an object of the same type. The case of maximal parabolic subgroups is studied in detail.

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✍ Corrado Marastoni 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 103 KB

Let G be a connected semisimple algebraic group over C, P a parabolic subgroup, g and p their Lie algebras. We prove a microlocal version of Gyoja's conjectures [2] about a relation between the irreducibility of generalized Verma modules on g induced from p and the zeroes of b-functions of P -semi-i