相关论文: Representations of Compact Lie Groups of Low Cohom…

We classify irreducible representations of compact connected Lie groups whose orbit space is isometric to the orbit space of a representation of a compact Lie group of dimension~$7$, $8$ or $9$. They turn out to be closely related to…

The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.

Several classes of irreducible orthogonal representations of compact Lie groups that are of importance in Differential Geometry have the property that the second osculating spaces of all of their nontrivial orbits coincide with the…

We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…

We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…

We suggest a method of constructing special nonunitary representations of semisimple Lie groups using representations of Iwasawa subgroups. As a typical example, we study the group $U(2,2)$.

We study isometric Lie group actions on the compact exceptional groups E6, E7, E8, F4 and G2 endowed with a biinvariant metric. We classify polar actions on these groups. We determine all isometric actions of cohomogeneity less than three…

We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then apply our…

We provide detailed calculations for the classification of representations of compact simple Lie groups with non-empty boundary in the orbit space, first announced in a previous paper [arXiv:2112.00513] by the same authors.

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

In this paper we give a characterization of the possible homology groups that can occur for compact simply connected cohomogeneity one manifolds in dimensions seven and lower.

We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…

In this paper we classify the reducible representations of compact simple Lie groups all of whose orbits are tautly embedded in Euclidean space with respect to Z_2 coefficients.

We introduce a remarkable subset "the stem" of the set of positive roots of a reduced root system. The stem determines several interesting decompositions of the corresponding reductive Lie algebra. It gives also a nice simple three…

We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

A cohomogeneity one manifold is a manifold with the action of a compact Lie group, whose quotient is one dimensional. Such manifolds are of interest in Riemannian geometry, in the context of nonnegative sectional curvature, as well as in…

We examine subgroups of locally compact groups that are continuous homomorphic images of connected Lie groups and we give a criterion for being such an image. We also provide a new characterisation of Lie groups and a characterisation of…

The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.