The symmetric spaces the title refers to are the spaces X = G=K where G is a connected semisimple Lie group with nite center and K is a maximal compact subgroup. The Fourier transform on X is deened by means of the Iwasawa decomposition G = NAK of G where N is nilpotent and A abelian. Let g; n; a; k denote the corresponding Lie algebras. We also need the group M = K A ; the centralizer of A in ...

Let X be an F -rational nilpotent element in the Lie algebra of a connected and reductive group G defined over the ground field F . One may associate toX certain cocharacters of Gwith favorable properties; this is an essential feature of the classification of geometric nilpotent orbits due to Bala-Carter, Pommerening, and, more recently, Premet. Suppose that the Lie algebra has a non-degenerate...

In Section 2, after giving the basic definitions and some elementary consequences, we introduce two fundamental algebraic structures associated with a coherent configuration, namely, the boolean algebra of admissable relations and the adjacency ring. The action of a group on a finite set induces the structure of a coherent configuration in the set, and in this situations, which we refer to as t...

Let f be a measure-preserving transformation of a Lebesgue space (X,μ) and let F be its extension to a bundle E = X × R by smooth fiber maps Fx : Ex → Efx so that the derivative of F at the zero section has negative Lyapunov exponents. We construct a measurable system of smooth coordinate changes Hx on Ex for μ-a.e. x so that the maps Px = Hfx ◦Fx ◦H−1 x are sub-resonance polynomials in a finit...

Let G be a complex reductive algebraic group and let Γ be a finitely generated group. We study properties of irreducible and completely reducible representations ρ : Γ → G in the context of the geometric invariant theory of the G action on the space of G-representations of Γ by conjugation. Let XG(Γ) be the G-character variety of Γ. We prove that if ρ : Γ → G is completely reducible and it repr...

group GC defined over Q whose connected component G 0 Q has no rational character. It is also necessary to suppose that the centralizer of a maximal Q split torus of G0C meets every component of GC. The reduction theory of Borel applies, with trivial modifications, to G; it will be convenient to assume that Γ has a fundamental set with only one cusp. Fix a minimal parabolic subgroup P 0 C defin...

Let X and Y be commuting nilpotent K-endomorphisms of a vector space V , where K is a field of characteristic p ≥ 0. If F = K(t) is the field of rational functions on the projective line P1/K , consider the K(t)-endomorphism A = X+ tY of V . If p = 0, or if A = 0, we show here that X and Y are tangent to the unipotent radical of the centralizer of A in GL(V ). For all geometric points (a : b) o...