Parabolically connected subgroups

I. V. Netai

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: All reductive spherical subgroups of the group $\operatorname{SL}(n)$ are found for which the intersections with every parabolic subgroup of $\operatorname{SL}(n)$ are connected. This condition guarantees that open equivariant embeddings of the corresponding homogeneous spaces into Moishezon spaces are algebraic.
Bibliography: 6 titles.

Keywords: reductive group, parabolic subgroup, spherical subgroup, flag, Moishezon space.

UDC: 512.743

MSC: Primary 20G20; Secondary 14L30, 14L35, 20G07, 32M05

Received: 16.05.2010 and 08.09.2010

DOI: 10.4213/sm7741

 English version: Sbornik: Mathematics, 2011, 202:8, 1169–1182

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