1 research outputs found
Schubert calculus of Richardson varieties stable under spherical Levi subgroups
We observe that the expansion in the basis of Schubert cycles for
of the class of a Richardson variety stable under a spherical Levi subgroup is
described by a theorem of Brion. Using this observation, along with a
combinatorial model of the poset of certain symmetric subgroup orbit closures,
we give positive combinatorial descriptions of certain Schubert structure
constants on the full flag variety in type . Namely, we describe
when and are inverse to Grassmannian permutations with unique descents
at and , respectively. We offer some conjectures for similar rules in
types and , associated to Richardson varieties stable under spherical
Levi subgroups of SO(2n+1,\C) and SO(2n,\C), respectively.Comment: Section 4 significantly shortened, and other minor changes made as
suggested by referees. Final version, to appear in Journal of Algebraic
Combinatoric