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A path model for geodesics in Euclidean buildings and its applications to representation theory
path model for geodesics Euclidean buildings representation theory
2015/10/14
In this paper we give a combinatorial characterization of projections ofgeodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex reductive Lie ...
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 ...
Unitary representations of real reductive groups
Unitary representations real reductive groups
2015/9/28
The purpose of this paper is to give a finite algorithm for computing the set of irreducible unitary representations of a real reductive Lie group G. Even before explaining the nature of the algorithm...
From double Lie groupoids to local Lie 2-groupoids
double Lie groupoids local Lie 2-groupoids
2011/2/22
We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger’s fundamental groupoid from the fundamental double groupoi...
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.
Higher Lie algebra actions on Lie algebroids
Lie algebroid NQ-manifold double Lie algebroid higher Lie algebra action
2011/1/17
We consider a simple instance of action up to homotopy. More precisely, we consider non-strict actions of DGLAs in degrees −1 and 0 on degree 1 NQ-manifolds. In a more conventional language this...
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...
Selected results on Lie supergroups and their radial operators
Selected results Lie supergroups radial operators
2011/2/25
Foundational material on complex Lie supergroups and their radial operators is presented. In particular, Berezin’s recursion formula for describing the radial parts of fundamental operators in general...
Reduce and Solve Boltzmann Equation on a Global Lie Group
Reduce Solve Boltzmann Equation Global Lie Group
2011/1/21
A global solution of Boltzmann equation is proposed after introducing a three-dimensional closed Lie group to simplify the collision term.
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...