This paper gives necessary and sufficient conditions for the centralizer of a finite subgroup of outer automorphisms (resp. automorphisms) of a finitely generated free group to be finite. If G is realized by its action on a graph, Krstić’s work produces generators of the centralizer of G in terms of graph isomorphisms and certain graph transformations. This paper examines the behavior of these ...

Let g be a complex semisimple Lie algebra, and let G be a complex semisimple group with trivial center whose root system is dual to that of g. We establish a graded algebra isomorphism H q (Xλ,C) ∼= Sg e/Iλ, where Xλ is an arbitrary spherical Schubert variety in the loop Grassmannian for G, and Iλ is an appropriate ideal in the symmetric algebra of g, the centralizer of a principal nilpotent in...

On the torus of dimension 2, 3, or 4, we show that the subset of diffeomorphisms with trivial centralizer in the C topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphism.

In this note, G is a compact connected Lie group. We are concerned with the torsion of the cohomology ring H*(G; Z) of G over the integers, certain commutative subgroups of G, and relations between these two questions. NOTATION. E(mi, • • • , mr) or £ A ( ^ I , • • • , mr) denotes the exterior algebra over the ring A of a free .4-module with r generators of respective degrees wi, • • • , mr; p ...

Let K be a compact connected Lie group and M a compact Hamiltonian K-manifold, i.e., a symplectic K-manifold equipped with a moment map μ : M → k. In this paper, we determine Col(M): the set of all functions on M which Poisson commute with all Kinvariant functions. For this, we construct a finite reflection group WM and show that Col(M) is completely determined by μ(M) and WM . More precisely, ...

We show that actions of finite-dimensional semisimple commutative Hopf algebras H on //-module algebras A are essentially group-gradings. Moreover we show that the centralizer of H in the smash product A # H equals A" ® H. Using these we invoke results about group graded algebras and results about centralizers of separable subalgebras to give connections between the ideal structure of A, A and ...

We give a new proof of Brink’s theorem that the nonreflection part of a reflection centralizer in a Coxeter group is free, and make several refinements. In particular we give an explicit finite set of generators for the centralizer and a method for computing the Coxeter diagram for its reflection part. In many cases, our method allows one to compute centralizers quickly in one’s head. We also d...

Let G be a connected reductive p-adic group and let g be its Lie algebra. LetO be a G-orbit in g. Then the orbital integral μO corresponding to O is an invariant distribution on g, and Harish-Chandra proved that its Fourier transform μ̂O is a locally constant function on the set g′ of regular semisimple elements of g. Furthermore, he showed that a normalized version of the Fourier transform is l...

Using the geometric Satake correspondence, Mirkovic-Vilonen cycles in affine Grasssmannian give bases for representations of a semisimple group G . We prove that these are perfect, i.e. compatible with action Chevelley generators positive half Lie algebra g. compute this terms intersection multiplicities Grassmannian. stitch together to basis C[N] regular functions on unipotent subgroup. multip...