An algebraic model for free rational G-spectra for connected compact Lie groups G

Classifying Rational G-Spectra for Finite G

We give a new proof that for a finite group G , the category of rational Gequivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in G , as H runs over the conjugacy classes of subgroups of G . Furthermore the Quillen equivalences of our proof are all symmetric monoidal. Thus we can unders...

Mean eigenvalues for simple, simply connected, compact Lie groups

We determine for each of the simple, simply connected, compact and complex Lie groups SU(n), Spin(4n+2) and E6 that particular region inside the unit disk in the complex plane which is filled by their mean eigenvalues. We give analytical parameterizations for the boundary curves of these so-called trace figures. The area enclosed by a trace figure turns out to be a rational multiple of π in eac...

The Orbit Method for Compact Connected Lie Groups

who had a major influence on my mathematical development and who always had time for me and my questions. I am especially indebted to Prof. Hilgert for his guidance. He encouraged me to spend a semester abroad and proposed the topic of this thesis to me. I am also grateful to the " Studienstiftung des deutschen Volkes " for two brilliant summer academies and the opportunity to meet a lot of gre...

An Algebraic Model for Rational Torus-equivariant Spectra

We show that the category of rational G-spectra for a torus G is Quillen equivalent to an explicit small and practical algebraic model, thereby providing a universal de Rham model for rational G-equivariant cohomology theories. The result builds on the Adams spectral sequence of [12], the enriched Morita equivalences of [23], and the functors of [27] making rational spectra algebraic.

On the Equivariant Homotopy of Free Abelian Groups on G-spaces and G-spectra