Let be a simple algebraic group and a parabolic subgroup of with abelian unipotent radical , and let be a Borel subgroup of contained in . Let be the Lie algebra of and a Levi factor of . Then is a Hermitian symmetric subgroup of and acts with finitely many orbits both on and on . In this paper we study the Bruhat order of the -orbits in and in , proving respectively a conjecture of Panyushev and a conjecture of Richardson and Ryan.
Cite this article
Jacopo Gandini, Andrea Maffei, The Bruhat order on Hermitian symmetric varieties and on abelian nilradicals. J. Eur. Math. Soc. 22 (2020), no. 10, pp. 3383–3416DOI 10.4171/JEMS/988