Séminaires : Séminaire sur les Algèbres Enveloppantes

Equipe(s) :
Responsables :J.-Y. Charbonnel, R. Rentschler, M. Varagnolo
Email des responsables : Jean-Yves Charbonnel <jyc@math.jussieu.fr>, Rudolf Rentschler <rent@math.jussieu.fr>, Michela Varagnolo <varagnol@math.u-cergy.fr>
Salle : 175 rue du Chevaleret - 75013 Paris
Adresse :
Description

Orateur(s) Gufang ZHAO - IMJ-PRG,
Titre Formal group laws and cohomology of quiver varieties.
Date31/10/2014
Horaire11:00 à 12:00
Diffusion
RésumeThis is a preliminary report on a work in progress. Coming from any formal group law, there is an oriented cohomology theory. It is expected that there is a quantum group associated to this formal group law, which acts on the corresponding cohomology theory applied to Nakajima quiver varieties. In this talk, I will describe some partial results in this direction, joint with Yang and Zhong. We prove that, for any formal group law, the formal affine Hecke algebra of Hoffnung-Malagon-Lopez-Savage-Zainoulline acts on the corresponding cohomology of the Springer fibers. Explicit formulae for the generalized Demazure-Lusztig operators are given. Also, we define a Hall algebra, generalizing the elliptic Hall algebra of Schiffmann-Vasserot, a.k.a., the shuffle algebra of Feigin-Odesskii. Then we prove that this algebra acts on the corresponding oriented cohomology of Nakajima quiver varieties. The Nakajima's raising operators are realized as elements in the Hall algebra.
Salle175 rue du Chevaleret - 75013 Paris
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