Related papers: Gelfand-Zeitlin actions and rational maps

Let G be a subgroup of finite index in SL(n,Z) for N > 4. Suppose G acts continuously on a manifold M, with fundamental group Z^n, preserving a measure that is positive on open sets. Further assume that the induced G action on H^1(M) is…

If A is an algebra of functions on X, there are many cases when X can be regarded as included in Hom(A,C) as the set of ring homomorphisms. In this paper the corresponding results for the symmetric products of X are introduced. It is shown…

Let $G$ be a complex semisimple Lie group and ${G}_{\mathbb R}$ a real form that contains a compact Cartan subgroup $T_{\mathbb R}$. Let $\pi$ be a discrete series representation of $G_{\mathbb R}$. We present geometric interpretations in…

We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known…

Let $G$ be a discrete countable infinite group. We show that each topological $(C,F)$-action $T$ of $G$ on a locally compact non-compact Cantor set is a free minimal amenable action admitting a unique up to scaling non-zero invariant Radon…

Let $G_{\P}$ be a compact simple Poisson-Lie group equipped with a Poisson structure $\P$ and $(M, \o)$ be a symplectic manifold. Assume that $M$ carries a Poisson action of $G_{\P}$ and there is an equivariant moment map in the sense of Lu…

Many of the existing results for closed Hamiltonian G-manifolds are based on the analysis of the corresponding Hamiltonian functions using Morse-Bott techniques. In general such methods fail for non-compact manifolds or for manifolds with…

On a Riemannian surface, the energy of a map into a Riemannian manifold is a conformal invariant functional, and its critical points are the harmonic maps. Our main result is a generalization of this theorem when the starting manifold is…

With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W-algebra of finite type. This algebra is obtained from the universal enveloping algebra U(g) by a certain Hamiltonian…

Let $GL_M$ be general linear Lie group over the complex field. The irreducible rational representations of the group $GL_M$ are labeled by pairs of partitions $\mu$ and $\tilde\mu$ such that the total number of non-zero parts of $\mu$ and…

In the paper we consider a realization of a finite dimensional irreducible representation of the Lie algebra $\mathfrak{gl}_n$ in the space of functions on the group $GL_n$. It is proved that functions corresponding to Gelfand-Tsetlin…

Consider the action of $SL(n+1,\mathbb{R})$ on $\mathbb{S}^n$ arising as the quotient of the linear action on $\mathbb{R}^{n+1}\setminus\{0\}$. We show that for a semigroup $\mathfrak{S}$ of $SL(n+1,\mathbb{R})$, the following are…

Given a C*-dynamical system (A,G,\alpha), we discuss conditions under which subalgebras of the multiplier algebra M(A) consisting of fixed points for \alpha are Morita-Rieffel equivalent to ideals in the crossed product of A by G. In case G…

The main purpose of this article is to extend some of the ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. Given a generic component of the…

We define formal geometric quantisation for proper Hamiltonian actions by possibly noncompact groups on possibly noncompact, prequantised symplectic manifolds, generalising work of Weitsman and Paradan. We study the functorial properties of…

We obtain an explicit characterization of the stable points of the action of G=SL(2,C) on the cartesian product G^n by simultaneous conjugation on each factor, in terms of the corresponding invariant functions, and derive from it a simple…

We consider compact symplectic manifolds acted on effectively by a compact connected Lie group $K$ in a Hamiltonian fashion. We prove that the squared moment map $||\mu||^2$ is constant if and only if $K$ is semisimple and the manifold is…

Let $G$ be a compact connected semisimple Lie group. We extend the techniques of Weinstein [W] to give a construction in group cohomology of symplectic forms $\omega$ on \lq twisted' moduli spaces of representations of the fundamental group…

We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric…

We know that $\mathbb{Z}_n$ is a finite field for a prime number $n$. Let $m,n$ be arbitrary natural numbers and let $\mathbb{Z}^m_n= \mathbb{Z}_n \times\mathbb{Z}_n\times...\times\mathbb{Z}_n$ be the Cartesian product of $m$ rings…