Jeudi 23 Mai 2013, 10:30 à IM-JUSSIEU-PRG, 2015	IMJ-CHE (Séminaire Claude Chevalley)	math.RT
Sarah Scherotzke	Graded quiver varieties and derived categories
Abstract:	Graded quiver varieties were invented by Nakajima to give a geometric construction of representations of quantum groups. They have also been used recently to construct monoidal categorifications of cluster algebras. Graded quiver varieties associated with a quiver Q are defined by geometric invariant theory. In my talk, I will explain how they can be described explicitly as modules of certain mesh categories. We show that there is a bijection between their strata and the isomorphism classes of objects in the derived category of the quiver Q. Under this bijection the degeneration order between strata corresponds to a degeneration order defined on the derived category by Jensen-Su-Zimmermann. Furthermore, we describe the fibers of the desingularisation map from the smooth quiver variety to the affine quiver variety as Grassmanianns of a representable functor of the derived category of Q. This is joint work with Bernhard Keller.

Jeudi 30 Mai 2013, 10:30 à IM-JUSSIEU-PRG, 2015	IMJ-CHE (Séminaire Claude Chevalley)	math.RT
Britta SpÄth	The inductive McKay condition for simple groups of type A
Abstract:	John McKay's conjecture (1970) is an elementary-looking global/local statement relating the representation theory of a group to the normalizer of its Sylow subgroup. After the reduction theorem for this conjecture given by Isaacs-Malle-Navarro (2007), it is sufficient to check a strong version of this conjecture, the so-called inductive McKay condition for all finite quasi-simple groups. We verify this condition for special linear groups and special unitary groups over finite fields. Key to the proofs is the study of (certain) generalized Gelfand-Graev representations. As a byporduct we obtain some surprising statements about all characters of those groups, for example that as stabilizer of a character of SL_n(q), only certain subgroups can occur.

Jeudi 6 Juin 2013, 10:30 à IM-JUSSIEU-PRG, 2015	IMJ-CHE (Séminaire Claude Chevalley)	math.RT
Sascha Orlik	The cohomology of Deligne-Lusztig varieties for the general linear group
Abstract:	In my talk I want to discuss an approach for determining the cohomology of Deligne-Lusztig varieties in the case of the general linear group. As a consequence we derive an inductive formula for the Tate twist -1-contribution in the cohomology of these varieties.