Casselman-Wallach property for homological theta lifting
Zhibin Geng, Hang Xue
TL;DR
This paper proves the Casselman-Wallach property for homological theta lifting over archimedean fields, enabling a well-defined Euler-Poincaré characteristic in the Grothendieck group of representations, using a novel filtration approach.
Contribution
It establishes the Casselman-Wallach property for homological theta lifting over archimedean fields, a significant advancement in representation theory.
Findings
Casselman-Wallach property is proven for homological theta lifting.
Euler-Poincaré characteristic is well-defined in the Grothendieck group.
Introduces a corank-one parabolic stable filtration on the Weil representation.
Abstract
In this paper, we establish the Casselman-Wallach property for homological theta lifting over archimedean local fields. As a consequence, the Euler-Poincar\'e characteristic is a well-defined element in the Grothendieck group of Casselman-Wallach representations. Our main tool is a corank-one parabolic stable filtration on the Weil representation.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory