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math.RT2026
A bar operation on the double affine Hecke algebra
Dougal Davis, Ivan Losev, Calder Morton-Ferguson
We construct a bar-type operation for the affine Hecke algebra $\Ha$ attached to a symmetrizable Kac--Moody group. Our main tool is a geometric bimodule defined using the equivaria…
math.RT2025
Hodge theory, intertwining functors, and the Orbit Method for real reductive groups
Dougal Davis, Lucas Mason-Brown
We study the Hodge filtrations of Schmid and Vilonen on unipotent representations of real reductive groups. We show that for various well-defined classes of unipotent representatio…
math.RT2024
The FPP Conjecture for Real Reductive Groups
Dougal Davis, Lucas Mason-Brown
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 properti…