Distributions of Positive Type and Representations of Lie Groups.
We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair. For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in...
By using the interplay between the Eulerian idempotent and the Dynkin idempotent, we construct explicitly a particular symmetric solution of the first equation of the Kashiwara-Vergne conjectureThen, we explicit all the solutions of the equation in the completion of the free Lie algebra generated by two indeterminates and thanks to the kernel of the Dynkin idempotent.
Generalizing the proof – by Hecht and Schmid – of Osborne’s conjecture we prove an Archimedean (and weaker) version of a theorem of Colette Moeglin. The result we obtain is a precise Archimedean version of the general principle – stated by the second author – according to which a local Arthur packet contains the corresponding local -packet and representations which are more tempered.