Publications associées à Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

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Central Subalgebras Of The Centralizer Of A Nilpotent Element

Donna Testerman

Let G be a connected, semisimple algebraic group over a field k whose characteristic is very good for G. In a canonical manner, one associates to a nilpotent element X is an element of Lie(G) a parabolic subgroup P - in characteristic zero, P may be descri ...

Amer Mathematical Soc2016

Diophantine properties of nilpotent Lie groups

A finitely generated subgroup F of a real Lie group G is said to be Diophantine if there is beta > 0 such that non-trivial elements in the word ball B-Gamma(n) centered at 1 is an element of F never approach the identity of G closer than broken vertical ba ...

London Mathematical Society, Cambridge2015

Distinguished unipotent elements and multiplicity-free subgroups of simple algebraic groups

Donna Testerman, Martin W. Liebeck

For G a simple algebraic group over an algebraically closed field of characteristic 0, we determine the irreducible representations ρ:G→I(V), where I(V) denotes one of the classical groups SL(V), Sp(V), SO(V), such that ρ sends some distinguished unipotent ...

2015

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Martins Bruveris, Martin Bauer

In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homogeneous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an ...

Springer Verlag2014

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

Martins Bruveris, Martin Bauer

This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics th ...

Springer Verlag2014

L-2-Betti numbers and Plancherel measure

Henrik Densing Petersen, Alain Valette

We compute L-2-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the L-2-Bet ...

Academic Press Inc Elsevier Science2014

Integrable G-strands on semisimple Lie groups

Tudor Ratiu, François Gay-Balmaz

The present paper derives systems of partial differential equations that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. It also determines the general form of Hamilton's principles and Hamiltonians for these s ...

Iop Publishing Ltd2014

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Martins Bruveris, Martin Bauer

The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...

Springer Verlag2013

Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

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Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Central Subalgebras Of The Centralizer Of A Nilpotent Element

Diophantine properties of nilpotent Lie groups

Dynamics of particles with anisotropic mass depending on time and position

Distinguished unipotent elements and multiplicity-free subgroups of simple algebraic groups

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

L-2-Betti numbers and Plancherel measure

Integrable G-strands on semisimple Lie groups

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Dynamics of particles with anisotropic mass depending on time and position

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Overview of the Geometries of Shape Spaces and Diffeomorphism Groups

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Central Subalgebras Of The Centralizer Of A Nilpotent Element

Distinguished unipotent elements and multiplicity-free subgroups of simple algebraic groups

Diophantine properties of nilpotent Lie groups

L-2-Betti numbers and Plancherel measure

Integrable G-strands on semisimple Lie groups

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II