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Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

Andrzej Daszkiewicz, Witold Kraśkiewicz, Tomasz Przebinda (2005)

Open Mathematics

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...

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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