Seules les adresses mails institutionnelles sont acceptées lors de la création d'un compte. La création de compte est modérée, merci d'attendre leur validation.
Only institutional email addresses will be accepted when asking for an account. Account creation is moderated, please wait until then.
Weekly seminars

Construction of Gelfand-Tsetlin modules for $gl(n)$

by Vyacheslav Futorny (Univ. Sao Paolo)

jeudi 22 juin 2017 de à (Europe/Paris)
at Annecy-le-Vieux ( Auditorium )
9 chemin de Bellevue 74940 ANNECY LE VIEUX
Description
A classical paper of  Gelfand  and  Tsetlin describes a basis of irreducible finite dimensional modules over the Lie algebra $gl(n)$.  This is one of the most remarkable results of the representation theory of  Lie algebras which initiated a development of  the theory of Gelfand-Tsetlin modules. The Gelfand-Tsetlin modules  form the largest subcategory of $gl(n)$-modules  (in particular, of weight modules with respect to a fixed Cartan subalgebra) where there is some understanding of irreducible modules. The main remaining problem is how to construct explicitly these modules. We propose a new effective method of constructing explicitly  Gelfand -Tsetlin modules for $gl(n)$ and obtain a large family of irreducible   modules  that have a basis consisting of Gelfand-Tsetlin tableaux and the action of the Lie algebra is given by the  Gelfand-Tsetlin formulas.  As an application of our construction we prove necessary and sufficient condition  for the Gelfand and Graev's continuation construction  to define a module which was conjectured by Lemire and Patera. The talk is based on recent joint results with Luis Enrique Ramirez and Jian Zhang.