5 citations · 15 across the 14 of their papers we have counts for
15 papers
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…
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…
Unipotent Representations of Complex Groups and Extended Sommers Duality
Lucas Mason-Brown, Dmytro Matvieievskyi, Shilin Yu
Let be a complex reductive algebraic group. In arXiv:2108.03453, we have defined a finite set of irreducible admissible representations of called `unipotent representations…
Wavefront Sets of Unipotent Representations of Reductive -adic Groups II
Dan Ciubotaru, Lucas Mason-Brown, Emile Okada
The wavefront set is a fundamental invariant of an admissible representation arising from the Harish-Chandra-Howe local character expansion. In this paper, we give a precise formul…
Some Unipotent Arthur Packets for Reductive -adic Groups
Dan Ciubotaru, Lucas Mason-Brown, Emile Okada
Let be a -adic field and let be the -points of a connected reductive group, inner to split. The set of Aubert-Zelevinsky duals of the constituents of a te…
The Wavefront Sets of Unipotent Supercuspidal Representations
Dan Ciubotaru, Lucas Mason-Brown, Emile Okada
Let be a semisimple -adic group, inner to split. In this article, we compute the algebraic and canonical unramified wavefront sets of the irreducible su…
Restricting Representations from a Complex Group to a Real Form
Lucas Mason-Brown
Let be a complex connected reductive algebraic group and let be a real form of . We construct a sequence of functors from admissible (resp.…
Arthur's Conjectures and the Orbit Method for Real Reductive Groups
Lucas Mason-Brown
The first half of this article is expository -- I will review, with examples, the main statements of the Langlands classification and Arthur's conjectures for real reductive groups…
Regular Functions on the K-Nilpotent Cone
Lucas Mason-Brown
Let be a complex reductive algebraic group with Lie algebra and let be a real form of with maximal compact subgroup . Associ…
Equivariant Vector Bundles on Varieties with Codimension-one Orbits
Lucas Mason-Brown, James Tao
Let be an algebraic group and let be a smooth -variety with two orbits: an open orbit and a a closed orbit of codimension . We give an algebraic description of the ca…
Wavefront Sets of Unipotent Representations of Reductive -adic Groups I
Dan Ciubotaru, Lucas Mason-Brown, Emile Okada
The wavefront set is a fundamental invariant arising from the Harish-Chandra-Howe local character expansion of an admissible representation. We prove a precise formula for the wave…
Unipotent Ideals for Spin and Exceptional Groups
Lucas Mason-Brown, Dmytro Matvieievskyi
In the monograph arXiv:2108.03453, we define the notion of a unipotent representation of a complex reductive group. The representations we define include, as a proper subset, all s…
Upper Triangularity for Unipotent Representations
Lucas Mason-Brown
Suppose is a real reductive group. The determination of the irreducible unitary representations of is one of the major unsolved problem in representation theory. There is e…
Unipotent Representations Attached to the Principal Nilpotent Orbit
Lucas Mason-Brown
In this paper, we construct and classify the special unipotent representations of a real reductive group attached to the principal nilpotent orbit. We give formulas for the $\mathb…
Unipotent Representations and Microlocalization
Lucas Mason-Brown
We develop a theory of microlocalization for Harish-Chandra modules, adapting a construction of Losev (\cite{Losev2011}). We explore the applications of this theory to unipotent re…