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In this paper we apply our results on the geometry of polygons in infinitesimal symmetric spaces, symmetric spaces and buildings, [KLM1, KLM2], to four problems in algebraic group theory. Two of these...
Let G be a non-compact connected semisimple Lie group of real rank one with finite center, K a maximal compact subgroup of G and X = G/K an associated symmetric space of real rank one. We will p...
Let X be a symmetric space of non-compact type or a locally finite, strongly transitive Euclidean building, and let B denote the geodesic boundary of X. We reduce the study of visual limits of maximal...
Abstract: Let N be a symmetric space of dimension n > 5 whose de Rham decomposition contains no factors of constant curvature and let W be the Weyl tensor of N at some point. We prove that a Riemannia...
There is a curious relation between two kinds of phase space distributions associated to Laplace-eigenfunctions ϕk on a compact hyperbolic manifold Y .
Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant poly-nomial.
In this paper we establish stability results for symmetric spaces of noncompact type under Ricci flow, i.e. we will show that any small perturbation of the symmetric metric is flown back to the origin...
The c-functions, related to a reductive symmetric space G/H and a fixed representation of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.
We give one more interpretation of the symbolic formulae $U(-N)=U(N)$ and $Sp(-2N)=SO(2N)$ by comparing the values of certain Casimir operators in the corresponding tensor representations. We show al...
We characterize the image of the Poisson transform on each boundary component of a Riemannian symmetric space of the noncompact type by a system of differential equations. The system corresponds to a...
We classify homotopes of classical symmetric spaces (studied in Part I of this work). Our classification uses the fibered structure of homotopes: they are fibered as symmetric spaces, with flat fibers...
Let X be a Riemannian symmetric space of the noncompact type. We prove that the solution of the time-dependent Schr\"odinger equation on X with square integrable initial condition f is identically ze...
We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions fo...
In this paper, we generalize Medos-Wang’s arguments and results on the mean curvature flow deformations of symplectomorphisms of CPn in [22] to complex Grassmann manifold G(n, n+m;C) and compact total...
We show that for every symmetric space G=K of compact type with K connected, the K-action on G=K by left translations is equivariantly formal.

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