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 : Zoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar
Adresse :Zoom ou IHP Salle 01

Le séminaire est prévu en présence à l'IHP et à distance. Pour les liens et mots de passe, merci de contacter l'un des organisateurs ou de souscrire à la liste de diffusion https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. L'information nécessaire sera envoyée par courrier électronique peu avant chaque exposé. Les notes et transparents sont disponibles ici.


Since March 23, 2020, the seminar has been taking place remotely. For the links and passwords, please contact one of the organizers or

subscribe to the mailing list at https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. The connexion information will be emailed shortly before each talk. Slides and notes are available here.


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.
SalleZoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar
AdresseZoom ou IHP Salle 01