Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Titre Zhelobenko operators, Schubert cells and q-W algebras
Horaire14:00 à 15:00
RésumeIn the beginning of the 80th Zhelobenko suggested a formula for a projection operator onto the subspace of singular vectors for modules from the BGG category O for a complex semisimple Lie algebra. This projection operator and some its modifications called Zhelobenko operators are related to the problem of finding an explicit description for the space of invariant regular functions with respect to the conjugation action of the unipotent radical of a semisimple algebraic group on the Borel subalgebra. In this talk I shall discuss a similar construction in case of the so-called q-W algebras which are related to the category of generalized Gelfand-Graev representations for quantum groups. The underlying geometry in this case is the geometry of the conjugation action of certain unipotent groups on Schubert cells. Using Zhelobenko operators I shall suggest an explicit description for generators of Poisson q-W algebras. Surprisingly, the results that will be presented in this talk have no direct analogues for complex semisimple Lie algebras and for ordinary W-algebras associated to them.