We study the effects of imposing linear relations within modules matrices on average sizes kernels. The that we consider can be described combinatorially in terms partial colourings grids. cells these grids correspond to positions and each defining relation involves all a given colour. prove such arising from ‘admissible’ has no effect kernels over finite quotients discrete valuation rings. Thi...

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 solve the following problem: Let M be a 2g × 2g symplectic matrix of prime order with integer entries. Find a unique normal form for M , that is, a symplectic matrix whose entries are determined by its conjugacy invariants. This is equivalent to finding a unique normal form for the matrix representation of the conjugacy class of a prime order element of the mapping class group.

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 ...

Solution. Henceforth, for the sake of notation when we must use variables, let i denote the element i+ k in the symmetric group on n elements, where i+ k ≤ n. S1 is the trivial group, so has one conjugacy class. S2 is abelian, so it has two conjugacy classes of one element each. We proved in class that cycle type is invariant under conjugation, so every conjugacy class may contain only one cycl...

We analyze a class of deformations of Anosov diffeomorphisms: these C-small, but C-macroscopic deformations break the topological conjugacy class but leave the high entropy dynamics unchanged. More precisely, there is a partial conjugacy between the deformation and the original Anosov system that identifies all invariant probability measures with entropy close to the maximum. We also establish ...

Affine Deligne-Lusztig varieties are analogs of DeligneLusztig varieties in the context of an affine root system. We prove a conjecture stated in the paper [5] by Haines, Kottwitz, Reuman, and the first named author, about the question which affine DeligneLusztig varieties (for a split group and a basic σ-conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a...

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...

The aim of this paper is to classify the finite nonsolvable groups in which every irreducible character of even degree vanishes on at most two conjugacy classes. As a corollary, it is shown that L2(2 f ) are the only nonsolvable groups in which every irreducible character of even degree vanishes on just one conjugacy class.

Random walk on the chambers of hyperplanes arrangements is used to de ne a family of card shu ing measuresMW;x for a nite Coxeter group W and real x 6= 0. By algebraic group theory, there is a map from the semisimple orbits of the adjoint action of a nite group of Lie type on its Lie algebra to the conjugacy classes of the Weyl group. Choosing such a semisimple orbit uniformly at random thereby...