Navigation: Home > Publications > Journal paper: Unipotent commutative group actions on flag varieties and nilpotent multiplications

 Journal paper: R. Devyatov, Unipotent commutative group actions on flag varieties and nilpotent multiplications

Abstract
Our goal is to classify all generically transitive actions of commutative unipotent groups on flag varieties up to conjugation. We establish a relationship between this problem and the classification of multiplications with certain properties on Lie algebra representations. Then we classify multiplications with the desired properties and solve the initial classification problem.
Final journal version
The final journal version is not available directly from this website due to copyright restrictions. It may be available here if your university or you have subscription. You can also request if from me by an email to deviatov at mccme dot ru, and I will send it to you.
First submitted version: download pdf; download zip archive with all sources
This version is slightly different from the previous one (which is available on arXiv), thanks to Michel Brion who brought my attention to some previously known results similar to intermediate lemmas I needed.
Version 11: download pdf; download zip archive with all sources
This is the version available on arXiv, as arXiv:1309.3480v1.
Bibliographic reference:
Rostislav Devyatov, Unipotent commutative group actions on flag varieties and nilpotent multiplications, Transformation Groups 20:1 (2015), 21–64.
Article page at the journal website

DOI: 10.1007/s00031-015-9306-0 (link)