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 Strictly transversal slices in algebraic groups and Lusztig's partition
Horaire14:00 à 15:00
RésumeIn this talk I shall show that for every conjugacy class in a complex semi-simple algebraic group G there is a strictly transversal slice Sg, i.e. an algebraic subvariety of G which intersects the class at an element g of G, and the codimension of the slice is equal to the dimension of the conjugacy class. The most general construction of slices transversal to conjugacy classes in algebraic groups was suggested by me in 2008. This construction generalizes the Steinberg cross-section to the set of regular conjugacy classes in algebraic groups. Recently Lusztig introduced a partition of G with a finite number of strata. It turns out that it suffices to verify the condition of strict transversality of the slices Sg for the conjugacy class Og of a single representative g in each stratum of Lusztig's partition. The finite family of the conjugacy classes Og contains all unipotent classes and possibly a few conjugacy classes of exceptional elements. In case of exceptional Lie groups verification of the strict transversality condition is based on a computer calculation (as well as the definition of Lusztig's partition). The construction of the slices Sg is used in the proof of De Concini-Kac-Procesi conjecture the algebraic part of which will be discussed in my talk on December 16.