6 papers
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…
Multivariate V-filtrations and the Strong Monodromy Conjecture for hyperplane arrangements
Dougal Davis, Ruijie Yang
In this work, we develop a new theory of multivariate V-filtration on D-modules along a simple normal crossing divisor and relate it with Sabbah's multi-filtration. We establish se…
On the Hodge and V-filtrations of mixed Hodge modules
Dougal Davis, Ruijie Yang
In this paper, we prove a Beilinson-type formula for the V-filtration of Kashiwara and Malgrange on a complex mixed Hodge module, using Hodge filtrations on the localization. Our f…
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…
Archimedean zeta functions, singularities, and Hodge theory
Dougal Davis, András C. Lőrincz, Ruijie Yang
We use Hodge theory to relate poles of the Archimedean zeta function of a holomorphic function with several invariants of singularities. First, we prove that the largest…
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…