An estimate of canonical dimension of groups based on Schubert calculus

Abstract

We sketch the proof of a connection between the canonical (0-)dimension of semisimple split simply connected groups and cohomology of their full flag varieties. Using this connection, we get a new estimate of the canonical (0-)dimension of simply connected split exceptional groups of type $E$ understood as a group.

arXiv commentFourth version, 22 pages, added Appendix A with more calculations and details of the proof of isomorphism of Picard groups (Proposition 3.2) using representation theory, the appendix with the proof using étale sheaves is now Appendix B