The FPP Conjecture for Real Reductive Groups

TL;DR

This paper proves the FPP conjecture for real reductive groups, establishing a significant upper bound on their unitary duals using advanced geometric and algebraic methods involving D-modules and Hodge filtrations.

Contribution

The paper introduces a novel proof of the FPP conjecture by applying global generation properties of D-modules and Hodge filtrations on flag varieties.

Findings

Established a strong upper bound on the unitary dual of real reductive groups.

Demonstrated the effectiveness of D-module techniques in representation theory.

Provided new insights into the structure of the unitary duals.

Abstract

In this paper, we prove the FPP conjecture, giving a strong upper bound on the unitary dual of a real reductive group. Our proof is an application of the global generation properties of $\mathcal{D}$-modules on the flag variety and their Hodge filtrations.