Related papers: Tempered homogeneous spaces III

We show that the Hodge filtration of a tempered Hodge module is generated by the lowest piece of its Hodge filtration. As a consequence, we prove the main conjecture of [SV] in the special case of tempered representations of real reductive…

Suppose $G$ is a connected complex Lie group and $H$ is a closed complex subgroup. Then there exists a closed complex subgroup $J$ of $G$ containing $H$ such that the fibration $\pi:G/H \to G/J$ is the holomorphic reduction of $G/H$, i.e.,…

Let k be a field, G a smooth connected linear algebraic group and X a homogeneous space of G over k, such that the geometric stabilizers are extensions of a smooth group of multiplicative type by a smooth connected characterfree group. If k…

We introduce an extended setting to study Hecke pairs $(G,H)$ which admit a regular representation on $L^2(H\backslash G)$, and consequently a $C^*$-algebra. As the result, many pairs of locally compact groups which had been studied in…

Let G be a semisimple group over an algebraically closed field of very good characteristic for G. In the context of geometric invariant theory, G. Kempf has associated optimal cocharacters of G to an unstable vector in a linear…

We exhibit explicit orthogonal decompositions of every multidimensional restricted root space of a real semi-simple Lie algebra. We then show a link between this result and a radiality property of smooth functions on G-homogeneous spaces…

Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H of G. In this note, we give a notion of G-complete reducibility -- G-cr for short --…

We develop Hodge theory for a Riemannian manifold $(M,g)$ with a background closed 3-form, H. Precisely, we prove that if the metric connections with torsion $\pm H$ have holonomy groups $G_\pm$, then the $d^H$-Laplacian preserves the…

We study second adjointness in the context of tempered admissible representations of a real reductive group. Compared to a recent result of Crisp and Higson, this generalizes from $SL_2$ to a general group, but specializes to only…

Let G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the ``order formula'' of D. Testerman…

We describe our conjecture about the irreducible unitary representations of reductive Lie groups, in the special case of $\mathrm{SL}(2,\mathbb{R})$.

The topological classification of gerbes, as principal bundles with the structure group the projective unitary group of a complex Hilbert space, over a topological space $H$ is given by the third cohomology $\text{H}^3(H, \Bbb Z)$. When $H$…

We detect Hilbert manifolds among isometrically homogeneous metric spaces and apply the obtained results to recognizing Hilbert manifolds among homogeneous spaces of the form G/H where G is a metrizable topological group and H is a closed…

We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R).

A group pair $(G, X)$ consists of a group $G$ together with a $G$-set $X$. Such a pair encodes properties of $G$ relative to the stabilisers of points in $X$. In this paper, we show how to combine properties of group pairs and their…

We study parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures, when G is a real reductive Lie group, and establish a correspondence between these objects and representations of the fundamental group of the punctured…

We consider actions of real Lie subgroups G of complex reductive Lie groups on Kaehlerian spaces. Our main result is the openness of the set of semistable points with respect to a momentum map and the action of G.

In this paper we prove that if G is a connected, simply-connected, semi-simple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra (Ug)_0 of the…

Given two algebraic groups $G$, $H$ over a field $k$, we investigate the representability of the functor of morphisms (of schemes) $\mathbf{Hom}(G,H)$ and the subfunctor of homomorphisms (of algebraic groups) $\mathbf{Hom}_{\rm gp}(G,H)$.…

Let G/P be a rational homogeneous variety, where P is a parabolic subgroup of a simple and simply connected linear algebraic group G defined over an algebraically closed field of characteristic zero. A homogeneous principal bundle over G/P…