Reductions of Invariant bi-Poisson Structures and Locally Free Actions

Flat Bi-Hamiltonian Structures and Invariant Densities

A bi-Hamiltonian structure is a pair of Poisson structures P , Q which are compatible, meaning that any linear combination αP+βQ is again a Poisson structure. A biHamiltonian structure (P,Q) is called flat if P and Q can be simultaneously brought to a constant form in a neighborhood of a generic point. We prove that a generic biHamiltonian structure (P,Q) on an odd-dimensional manifold is flat ...

Invariant Polynomials for Multiplicity Free Actions

This work concerns linear multiplicity free actions of the complex groups GC = GL(n,C), GL(n,C) × GL(n,C) and GL(2n,C) on the vector spaces V = Sym(n,C), Mn(C) and Skew(2n,C). We relate the canonical invariants in C[V ⊕ V ∗] to spherical functions for Riemannian symmetric pairs (G,K) where G = GL(n,R), GL(n,C) or GL(n,H) respectively. These in turn can be expressed using three families of class...

SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

G-Invariant Deformations of Almost-Coupling Poisson Structures

On a foliated manifold equipped with an action of a compact Lie group G, we study a class of almost-coupling Poisson and Dirac structures, in the context of deformation theory and the method of averaging.

Invariant Representation of Propagation Properties for Bi-coupled Periodic Structures