Related papers: An Integration Formula for Polar Actions

We show that integration over a $G$-manifold $M$ can be reduced to integration over a minimal section $\Sigma$ with respect to an induced weighted measure and integration over a homogeneous space $G/N$. We relate our formula to integration…

We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In…

We prove that the orbits of a polar action of a compact Lie group on a compact rank one symmetric space are tautly embedded with respect to Z_2-coefficients.

The Weyl integration model presented by An and Wang can be effectively used to reduce the integration over $G$-space. In this paper, we construct an especial Weyl integration model for KAK decomposition of Reductive Lie Group and obtain an…

We classify infinitesimally polar actions on compact Riemannian symmetric spaces of rank one. We also prove that every polar action on one of those spaces has the same orbits as an asystatic action.

The main result of the paper is the complete classification of the compact connected Lie groups acting coisotropically on complex Grassmannians. This is used to determine the polar actions on the same manifolds.

In this note we reformulate the spectral side of the Weyl law in the language of the matrix-valued quantisation on compact Lie groups.

We will provide a lower bound for the equivariant Lusternik-Schnirelmann category of an arbitrary proper action in terms of the stratification by orbit types, and an upper bound for proper polar actions in terms of the equivariant…

We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry…

Let $G$ be a Lie group acting properly on a smooth manifold $M$. If $M/G$ is connected, then we exhibit some simple and basic constructions for proper actions. In particular, we prove that the reduction principle in compact transformation…

We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar…

We obtain the full classification of coisotropic and polar actions of compact Lie group on irreducible Hermitian symmetric spaces.

We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally compact groups possessing large…

We show that polar actions of cohomogeneity two on simple compact Lie groups of higher rank, endowed with a biinvariant Riemannian metric, are hyperpolar. Combining this with a recent result of the second-named author, we are able to prove…

A group action is called polar if there exists an immersed submanifold (a section) which intersects all orbits orthogonally. Such group actions have been studied extensively on symmetric spaces. We show how to construct a manifold admitting…

We analyze polar actions on Hermitian and quaternion-K\"ahler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries…

Matrix Lie groups provide a language for describing motion in such fields as robotics, computer vision, and graphics. When using these tools, we are often faced with turning infinite-series expressions into more compact finite series (e.g.,…

In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…

We generalize I. Frenkel's orbital theory for non twisted affine Lie algebras to the case of twisted affine Lie algebras using a character formula for certain non-connected compact Lie groups.

The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character…