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Eulerian idempotent and Kashiwara-Vergne conjecture

Emily Burgunder (2008)

Annales de l’institut Fourier

By using the interplay between the Eulerian idempotent and the Dynkin idempotent, we construct explicitly a particular symmetric solution ( F , G ) of the first equation of the Kashiwara-Vergne conjecture x + y - log ( e y e x ) = ( 1 - e - ad x ) F ( x , y ) + ( e ad y - 1 ) G ( x , y ) . Then, we explicit all the solutions of the equation in the completion of the free Lie algebra generated by two indeterminates x and y thanks to the kernel of the Dynkin idempotent.

Exponents in Archimedean Arthur packets

Nicolas Bergeron, Laurent Clozel (2013)

Annales de l’institut Fourier

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 L -packet and representations which are more tempered.

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