Ein Kriterium für die formale Selbstadjungiertheit des Dirac-Operators
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.