K-orbits on G/B and Schubert constants for pairs of signed shuffles in types C and D

Abstract

We give positive descriptions for certain Schubert structure constants $c_{u,v}^w$ for the full flag variety in Lie types $C$ and $D$. This is accomplished by first observing that a number of the $K=GL(n,\C)$-orbit closures on these flag varieties coincide with Richardson varieties, and then applying a theorem of M. Brion on the decomposition of such an orbit closure in the Schubert basis in terms of paths in the weak order graph.

24 pages. Final version, published in J. Algebra

Cited by in corpus (6)

• Schubert calculus of Richardson varieties stable under spherical Levi subgroups
• Symmetric subgroup orbit closures on flag varieties: Their equivariant geometry, combinatorics, and connections with degeneracy loci
• Atoms for signed permutations
• The genesis of involutions (polarizations and lattice paths)
• $DIII$ clan combinatorics for the orthogonal Grassmannian
• Combinatorial results on (1,2,1,2)-avoiding $GL(p,\mathbb{C})\times GL(q,\mathbb{C})$-orbit closures on $GL(p+q,\mathbb{C})/B$