Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...

Let X be a locally compact Hausdorff space with n proper continuous self maps τ i : X → X for 1 ≤ i ≤ n. To this we associate various topological conjugacy algebras; and two emerge as the natural candidates for the universal algebra of the system, the tensor algebra A(X, τ) and the semicrossed product C 0 (X) × τ F + n. The C*-envelope of A(X, τ) is the Cuntz-Pimsner algebra C * (X, τ) as defin...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...

Holroyd, F.C., Reconstructing finite group actions and characters from subgroup information, Discrete Mathematics 110 (1992) 283-287. A finite group G is said to be action reconstructible if, for any action of G on a finite set, the numbers of orbits under restriction to each subgroup always give enough information to reconstruct the action up to equivalence. G is character reconstructible if, ...

Let H,,(q) be the Iwahori-Hecke algebra of the symmetric group S,,. Let F, be a finite field with y elements and let B be the Bore1 subgroup of upper triangular matrices in the general linear group G = GL,(F,). Let 1: denote the trivial representation of B induced to G. Then H,,(q) has a natural action on 1; that commutes with the G-action, and we define the bitrace btr(g, a) to be the trace of...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. A separability hypothesis appears in many general t...

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general...

Let (G,B,N, S) be a Tits system. Some aspects of intersections of conjugacy classes ofG with Bruhat cellsBẇB have been investigated by several authors (see e.g., [St1], [K], [V] and [VS]). Here w ∈ W = N/(B ∩N) and ẇ ∈ N is a preimage of w with respect to the natural surjection N → W . In particular, it is desirable to learn how a conjugacy class C of G is related to those conjugacy classes Cw ...