相关论文: Compact groups and their representations

There has been some work in the literature on limit theorems for the trace of commutators for compact Lie groups. We revisit this from the perspective of combinatorial representation theory.

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

In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…

We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to…

These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.

This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006) and follows its referencing guidelines.

To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.

We survey different tools to classify representations of compact Lie groups according to their cohomogeneity and apply these methods to the case of irreducible representations of cohomogeneity 6, 7 and 8.

We show how a polar representation of a compact connected Lie group can be linearly determined from its dimension and isotropy subgroup data in the general reducible case.

In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on elemental a la teor\'ia de representaciones…

This is a survey of results on partially commutative groups and partially commutative algebras.

New continuous group transforms, together with their discretization over a lattice of any density and admissible symmetry, are defined for a general compact simple Lie groups of rank $2\leq n<\infty$. Rank 1 transforms are known. Rank 2…

This is an expository paper (in Spanish) about the metric approximation of groups.

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…

This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.

A surface group representation into a Lie group is called totally elliptic if every simple closed curve on the surface is mapped to an elliptic element of the target group. In this note, we characterize all totally elliptic surface group…

In this book, I explored differential equations for operation in Lie group and for representations of group Lie in a vector space.

A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…

In math.SG/0303255, we discussed the connected components of the space of surface group representations for any compact connected semisimple Lie group and any closed compact (orientable or nonorientable) surface. In this sequel, we…

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…