Representations des groupes reductifs et sujets connexes – REPRED
The general purpose of this project is the study of various aspects of the representation theory of reductive groups (possibly over finite fields). We propose to focus on three main aspects: 1. Double affine Grassmannians and representations of Kac-Moody groups: the aim here is to extend previous work on the geometric Satake correspondence by Beilinson, Drinfeld and Lusztig by replacing the affine Grassmannian by the double affine Grassmannian and reductive groups by Kac-Moody groups. We intend to continue work by Baumann, Gaussent and Schiffmann. 2. Modular perverse sheaves: l-adic perverse sheaves proved to be a powerful tool in the representation theory of reductive groups and related areas. It is expected that modular perverse sheaves will play a fundamental role in modular representation theory. Here we intend to continue Juteau's work on the modular Springer correspondence. 3. Representation varieties and generalizations: The purpose of this theme is to understand the connections between the geometry of various moduli spaces involved in the Riemann-Hilbert correspondence and representation theory of reductive groups and Kac-Moody algebras. We intend to continue the work of Boalch, Hausel-Letellier-Villegas, Marin and Ressayre.
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Beginning and duration of the scientific project: - 0 Months