On properties of the Casselman-Jacquet functor
Alexander Yom Din
TL;DR
This thesis explores the properties of the Casselman-Jacquet functor, introducing a new approach to establish its adjoint relationship with the Bernstein functor and providing D-module explanations for related filtrations.
Contribution
It presents a novel technical method to show the Casselman-Jacquet functor as right adjoint to the Bernstein functor and offers D-module insights into the Bruhat filtration.
Findings
Casselman-Jacquet functor shown as right adjoint to Bernstein functor
D-module explanation of Bruhat filtration
Recorded conjectures on related properties
Abstract
In this thesis, we study the Casselman-Jacquet functor. We discuss a new technical approach which makes the Casselman-Jacquet functor right adjoint to the Bernstein functor. We give an explanation, using D-modules, of the Bruhat filtration appearing on the module obtained by applying the Casselman-Jacquet functor to a principal series representation. We record some conjectures.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Nonlinear Waves and Solitons