Let G be a connected reductive affine algebraic group defined over the complex numbers, and K ⊂ G be a maximal compact subgroup. Let X, Y be irreducible smooth complex projective varieties and f : X → Y an algebraic morphism, such that π1(Y ) is virtually nilpotent and the homomorphism f∗ : π1(X)→ π1(Y ) is surjective. Define R ( π1(X), G ) = {ρ ∈ Hom ( π1(X), G ) | A ◦ ρ factors through f∗} , ...

Abstract Let G be a simple algebraic group of adjoint type over an algebraically closed field k bad characteristic. We show that its sheets conjugacy classes are parametrized by -conjugacy pairs $(M,{\mathcal O})$ where M is the identity component centralizer semisimple element in and ${\mathcal O}$ rigid unipotent class , analogy with good characteristic case.

Let G be a quasi-split connected reductive group over a local eld of characteristic 0, and x a regular nilpotent element in the Lie algebra g of G. A theorem of Kostant then provides a canonical conjugacy class within each stable conjugacy class of regular semisimple elements in g. Normalized transfer factors take the value 1 on these canonical conjugacy classes. 1. Introduction Let k 0 be a lo...

Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class Φ(C) of G. In this paper we show that Φ(C) can be characterized in terms of the closure relations between unipotent classes. Previously, the analogous result was known ...

Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class Φ(C) of G. In this paper we show that Φ(C) can be characterized in terms of the closure relations between unipotent classes. Previously, the analogous result was known ...

We describe the isomorphism class of the torus centralizing a regular, semi-simple, stable conjugacy class in a simply-connected, semi-simple group. Let k be a field, and let G be a semi-simple, simply-connected algebraic group, which is quasi-split over k. The theory of semi-simple conjugacy classes in G is well understood, from work of Steinberg [S] and Kottwitz [K]. Any semi-simple conjugacy...

What ingredients are necessary to describe all maximal subgroups of the general finite group G? This paper is concerned with providing such an analysis. A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal subgroup N of G correspond, under the natural projection, to the maximal subgroups of the quotient...

Frey and Kani put a particular modular space structure on the space of a space of modular curves that resembles a Hurwitz space structure. We follow up on this, simplifying the group theory so that properties of this space are clear. For the rst, Prop. 2.4 shows it is simple to characterize the monodromy group of Frey-Kani covers of degree N (and that it is S N). In anticipation of other proble...

We give another proof of an observation of Thévenaz [4] and present a fusion system version of it. Namely, for a saturated fusion system F on a finite p-group S, we show that the number of the F-conjugacy classes of cyclic subgroups of S is equal to the rank of certain square matrices of numbers of orbits, coming from characteristic bisets, the characteristic idempotent and finite groups realiz...