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Invariant functions on Lie groups and Hamiltonian flows ofsurface group representations
Lie groups Hamiltonian flows
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2015/9/29
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...
CHARACTERISTIC CLASSES AND REPRESENTATIONS OF DISCRETE SUBGROUPS OF LIE GROUPS
CHARACTERISTIC CLASSES REPRESENTATIONS
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2015/9/29
(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 ...
Examples of the Atlas of Lie Groups and Representations
the Atlas Lie Groups Representations
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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 ...
Real-Variable Theory and Fourier Integral Operators on Semisimple Lie Groups and Symmetric Spaces of Real Rank One
Real-Variable Theory Fourier Integral Operators Semisimple Lie Groups Symmetric Spaces Real Rank One
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2014/4/3
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...
Martingale transform and Levy Processes on Lie Groups
Martingale transform Levy Processes Lie Groups Probability
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2012/6/29
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...
On the existence of nilsolitons on 2-step nilpotent Lie groups
existence nilsolitons 2-step nilpotent Lie groups Differential Geometry
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2012/4/16
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...
Special representations of nilpotent Lie groups and the associated Poisson representations of current groups
Current group canonical representation special representation
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2012/4/18
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...
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
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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 $F_4, E_6$ $E_7$
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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
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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
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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 Analysis and Nilpotent Lie Groups
Classical Analysis Nilpotent Lie Groups
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2011/1/19
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
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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
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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
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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...