JournalsjemsVol. 22, No. 10pp. 3383–3416

The Bruhat order on Hermitian symmetric varieties and on abelian nilradicals

  • Jacopo Gandini

    Università di Bologna, Italy
  • Andrea Maffei

    Università di Pisa, Italy
The Bruhat order on Hermitian symmetric varieties and on abelian nilradicals cover
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Abstract

Let GG be a simple algebraic group and PP a parabolic subgroup of GG with abelian unipotent radical PuP^u, and let BB be a Borel subgroup of GG contained in PP. Let pu\mathfrak {p^u} be the Lie algebra of PuP^u and LL a Levi factor of PP. Then LL is a Hermitian symmetric subgroup of GG and BB acts with finitely many orbits both on pu\mathfrak {p^u} and on G/LG/L. In this paper we study the Bruhat order of the BB-orbits in pu\mathfrak {p^u} and in G/LG/L, 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. 3383–3416

DOI 10.4171/JEMS/988