The Plancherel theorem for general semisimple groups
The Poisson boundary of random rational affinities
We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all -adic fileds.
The Poisson Kernel for Heisenberg Polynomials on the Disk.
The Poisson Space of the Koranyi Ball.
The Poisson Transform for Split Reductive Symmetric Spaces.
The Primitive Ideal Space of Solvable Lie Groups.
The principal series for a reductive symmetric space. I. -fixed distribution vectors
The proportionality constant for the simplicial volume of locally symmetric spaces
We follow ideas going back to Gromov's seminal article [Publ. Math. IHES 56 (1982)] to show that the proportionality constant relating the simplicial volume and the volume of a closed, oriented, locally symmetric space M = Γ∖G/K of noncompact type is equal to the Gromov norm of the volume form in the continuous cohomology of G. The proportionality constant thus becomes easier to compute. Furthermore, this method also gives a simple proof of the proportionality principle for arbitrary manifolds.
The quantum double of a (locally) compact group.
The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra
Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
The quasi-isometry classification of rank one lattices
The rectifiable distance in the unitary Fredholm group
Let = u: u unitary and u-1 compact stand for the unitary Fredholm group. We prove the following convexity result. Denote by the rectifiable distance induced by the Finsler metric given by the operator norm in . If and the geodesic β joining u₀ and u₁ in satisfy , then the map is convex for s ∈ [0,1]. In particular, the convexity radius of the geodesic balls in is π/4. The same convexity property holds in the p-Schatten unitary groups = u: u unitary and u-1 in the p-Schatten class...
The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces
The Representation of Inertial Particles in the Lie Algebra of the Lorentz Group
The representation theory of the Temperley-Lieb algebras.
The representation-ring of a compact Lie group
The Restriction of Admissible Representations to n.
The restriction to of a supercuspidal representation of
The Rockland condition for nondifferential convolution operators II
The -curvature of homogeneous -metrics.