This article explores the relationship between Hessenberg varieties associated with
semisimple operators with two eigenvalues and orbit closures of a spherical subgroup of the …

By explicitly describing a cellular decomposition we determine the Borel invariant cycles that
generate the Chow groups of the quotient of a reductive group by a Levi subgroup. For …

There is a natural analogue of weak Bruhat order on the involutions in any Coxeter group.
The saturated chains of intervals in this order correspond to reduced words for a certain set …

We examine Borel subgroup orbits in the classical symmetric space of type CI, which are
parametrized by skew symmetric (n, n)-clans. We describe bijections between such clans …

Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties,
the horospherical actions are determined. This leads to a characterization of the toroidal and …

This thesis examines the geometry and combinatorics of Borel subgroup orbits in classical
symmetric spaces G/L where G is complex linear algebraic group and L is a Levi factor of a …

Borel subgroup orbits of the classical symmetric space $ SO_ {2n}/GL_n $ are parametrized
by $ DIII $$(n, n) $-clans. We group the clans into" sects" corresponding to Schubert cells of …

Borel subgroup orbits of the classical symmetric space SO2n/GLn are parametrized by (n, n)-
clans of type DIII. We describe explicit bijections between such clans, diagonally symmetric …