Hodge Filtrations on Tempered Hodge Modules
Dougal Davis, Kari Vilonen
TL;DR
This paper proves that the Hodge filtration of tempered Hodge modules is generated by its lowest piece, leading to a proof of a key conjecture for tempered representations of real reductive Lie groups.
Contribution
It establishes that the Hodge filtration is generated by the lowest piece for tempered Hodge modules, confirming a main conjecture in a special case.
Findings
Hodge filtration of tempered Hodge modules is generated by the lowest piece
Main conjecture of [SV] is proved for tempered representations
Advances understanding of Hodge structures in representation theory
Abstract
We show that the Hodge filtration of a tempered Hodge module is generated by the lowest piece of its Hodge filtration. As a consequence, we prove the main conjecture of [SV] in the special case of tempered representations of real reductive Lie groups.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models