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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 ...
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...
Generalizing a construction of Wolfgang L\"uck and Bob Oliver, we define a good equivariant cohomology theory on the category of proper G-CW complexes when G is an arbitrary Lie group (possibly non-c...
We find an infinitesimal description of invariant generalized complex structures on Lie groups. We develop a systematic treatment of a class (called regular) of invariant generalized complex structure...
We study in this article some Sobolev-type inequalities on polynomial volume growth Lie groups. We show in particular that improved Sobolev inequalities can be extended without the use of the Littlew...
For G an arbitrary unimodular Lie group, we construct strongly continuous unitary representations of G in the Bergman space of a naturally constructed strongly pseudoconvex neighborhood of the complex...
An SKT metric is an Hermitian metric on a complex manifold whose fundamental 2-form ! satisfies @@! = 0. Streets and Tian introduced in [STb] a Ricci-type flow that preserves the SKT condition.
In this work we investigate solvable and nilpotent Lie groups with special metrics. The metrics of interest are left-invariant Einstein and algebraic Ricci soliton metrics. Our main result shows that ...

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