Clifford algebras, symmetric spaces and cohomology rings of Grassmannians

Date/heure
16 novembre 2023
13:45 - 14:45

Lieu
Salle de conférences Nancy

Oratrice ou orateur
Pavle Pandzic (Zagreb)

Catégorie d'évènement
Séminaire Théorie de Lie, Géométrie et Analyse


Résumé

We study various kinds of Grassmannians or Lagrangian Grassmannians over RC or H, all of which can be expressed as G/P where G is a classical group and P is a parabolic subgroup of G with abelian unipotent radical. The same Grassmannians can also be realized as (classical) compact symmetric spaces G/K. We give explicit generators and relations for the de Rham cohomology rings of G/P=G/K. At the same time we describe certain filtered deformations of these rings, related to Clifford algebras and spin modules. While the cohomology rings are of our primary interest, the filtered setting of K-invariants in the Clifford algebra actually provides a more conceptual framework for the results we obtain. This is joint work with Kieran Calvert and Kyo Nishiyama.