Hodge Filtrations on Tempered Hodge Modules

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.

9 pages. Minor changes to improve the clarity of the exposition (v2). Added a conceptual overview to the introduction (v3)