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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 ...
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 ...
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...
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...
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.
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 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...
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...
A global solution of Boltzmann equation is proposed after introducing a three-dimensional closed Lie group to simplify the collision term.
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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