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Examples of the Atlas of Lie Groups and Representations
the Atlas Lie Groups Representations
2015/9/28
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 ...
Kernels of Linear Representations of Lie Groups, Locally Compact Groups, and Pro-Lie Groups
Kernels of Linear Representations of Lie Groups Locally Compact Groups Pro-Lie Groups
2011/1/17
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.
Fixed points subgroups by two involutive automorphisms $\sigma, \gamma$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$
Fixed points subgroups by two involutive automorphisms $\sigma \gamma$ of compact exceptional Lie groups $F_4, E_6$ $E_7$
2011/2/21
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 ...
Decomposition of spinor groups by the involution σ' in exceptional Lie groups
Decomposition of spinor groups involution σ' in exceptional Lie groups
2011/2/22
The compact exceptional Lie groups F4,E6,E7 and E8 have spinor groups as a subgroup as follows.
Half-flat structures on decomposable Lie groups
Half-flat structures decomposable Lie groups
2011/2/22
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...
Half-space theorems and the embedded Calabi-Yau problem in Lie groups
Minimal surface constant mean curvature H-surface
2011/1/20
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...
Zeta-functions of weight lattices of compact semisimple connected Lie groups
Zeta-functions compact semisimple connected Lie groups
2010/11/8
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 ...
On duality and negative dimensions in the theory of Lie groups and symmetric spaces
duality negative dimensions theory Lie groups symmetric spaces
2010/11/8
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...
Equivariant K-theory for proper actions of non-compact Lie groups
Equivariant K-theory proper actions non-compact Lie groups
2010/11/8
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 study three natural bi-invariant partial orders on a certain covering group of the automorphism group of a bounded symmetric domain of tube type; these orderings are defined using the geometry of ...
Invariant generalized complex structures on Lie groups
Invariant generalized complex structures Lie groups
2010/11/30
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...
Some functional inequalities on polynomial volume growth Lie groups
Sobolev inequalities polynomial volume growth Lie groups
2010/12/7
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...
Unitary representations of unimodular Lie groups in Bergman spaces
Unitary representations of unimodular Lie groups Bergman spaces
2010/12/3
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.