English

An estimate of canonical dimension of groups based on Schubert calculus

Algebraic Geometry 2025-03-06 v3 Group Theory Representation Theory

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 EE understood as a group.

Keywords

Cite

@article{arxiv.2011.00950,
  title  = {An estimate of canonical dimension of groups based on Schubert calculus},
  author = {Rostislav Devyatov},
  journal= {arXiv preprint arXiv:2011.00950},
  year   = {2025}
}

Comments

Third version, 18 pages, an alternative proof of isomorphism of Picard groups (Proposition 3.2), using \'etale sheaves, is added as an appendix (while the previous proof, using representation theory, is also kept), some minor improvements are also made and some typos are also fixed