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In [7] it wasshown that ifn isthe fundamental group ofa closed oriented surface S and Gis Lie group satisfying very general conditions, then the space Hom(n, G)/G of conjugacy classes of representat...
(For convenience we shall henceforth assume that n is torsionfree: by Selberg's lemma [12] this may be accomplished by replacing TT by a subgroup of finite index. This insures that M is a compact ...
The Atlas of Lie Groups and Representations is a project in representation theory of real reductive groups. Themain goal of the atlas computer software, currently under development, is to compute the ...
Let G be a non-compact connected semisimple Lie group of real rank one with finite center, K a maximal compact subgroup of G and X = G/K an associated symmetric space of real rank one. We will p...
This paper constructs a class of martingale transforms based on L\'evy processes on Lie groups. From these, a natural class of bounded linear operators on the $L^p$-spaces of the group (with respect t...
A 2-step nilpotent Lie algebra n is said to be of type (p,q)if dim(n)=p+q and dim([n,n])=p. By considering a class of 2-step nilpotent Lie algebras naturally attached to graphs, we prove that there ex...
In this paper we describe the new model of the representations of the current groups with a semisimple Lie group of the rank one. In the earlier papers of 70-80-th (Araki, Gelfand-Graev-Vershik) had p...
For a topological group G the intersection KOR(G) of all kernels of ordinary representations is studied. We show that KOR(G) is contained in the center of G if G is a connected pro-Lie group.
For simply connected compact exceptional Lie groups G = F4,E6 and E7, we consider two involutions σ, γ and determine the group structure of subgroups G,of G which are the intersection G ∩ G of the ...
The compact exceptional Lie groups F4,E6,E7 and E8 have spinor groups as a subgroup as follows.
Half-flat SU(3)-structures are the natural initial values for Hitchin’s evolution equations whose solutions define parallel G2-structures.
Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I’ll describe how this goes for nilpotent Lie groups, for a class of Riemannian manifolds close...
We study the embedded Calabi-Yau problem for complete embedded constant mean curvature surfaces of finite topology or of positive injectivity radius in a simply-connected three-dimensional Lie group X...
We define zeta-functions of weight lattices of compact semisimple connected Lie groups. If the group is simply-connected, these zeta-functions coincide with ordinary zeta-functions of root systems of ...
We give one more interpretation of the symbolic formulae $U(-N)=U(N)$ and $Sp(-2N)=SO(2N)$ by comparing the values of certain Casimir operators in the corresponding tensor representations. We show al...

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