Partial Dirac cohomology and tempered representations

Elliptic Representations, Dirac Cohomology and Endoscopy To David, with admiration

Semipurity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the stu...

Tempered Representations and Nilpotent Orbits

Given a nilpotent orbit O of a real, reductive algebraic group, a necessary condition is given for the existence of a tempered representation π such that O occurs in the wave front cycle of π. The coefficients of the wave front cycle of a tempered representation are expressed in terms of volumes of precompact submanifolds of an affine space.

Dirac Cohomology for the Cubic Dirac Operator

Let g be a complex semisimple Lie algebra and let r ⊂ g be any reductive Lie subalgebra such that B|r is nonsingular where B is the Killing form of g. Let Z(r) and Z(g) be, respectively, the centers of the enveloping algebras of r and g. Using a Harish-Chandra isomorphism one has a homomorphism η : Z(g) → Z(r) which, by a well-known result of H. Cartan, yields the the relative Lie algebra cohom...

Tempered Representations and the Theta Correspondence

Let V be an even dimensional nondegenerate symmetric bilinear space over a nonarchimedean local field F of characteristic zero, and let n be a nonnegative integer. Suppose that σ ∈ Irr(O(V )) and π ∈ Irr(Sp(n, F )) correspond under the theta correspondence. Assuming that σ is tempered, we investigate the problem of determining the Langlands quotient data for π. Let F be a nonarchimedean local f...