Benjamin J. Wyser

Chains in weak order posets associated to involutions

The W -set of an element of a weak order poset is useful in the cohomological study of the closures of spherical subgroups in generalized flag varieties. We explicitly describe in a purely combinatorial manner the W -sets of three different weak order posets: the set of all involutions in the symmetric group, the set of fixed point free involutions of the symmetric group, and the set of charged involutions. These distinguished sets of involutions parametrize Borel orbits in the classical symmetric spaces associated to the general linear group. In particular, we characterize the maximal chains of an arbitrary lower order ideal in any of these three posets.

K -Orbit Closures on G / B as Universal Degeneracy Loci for Flagged Vector Bundles with Symmetric or Skew-Symmetric Bilinear Form

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of K-orbit closures on the flag variety G/B, where G = GL(n,

POLYNOMIALS FOR SYMMETRIC ORBIT CLOSURES IN THE FLAG VARIETY

\mathbb{C}

Wonderful Symmetric Varieties and Schubert Polynomials

), and where K is one of the symmetric subgroups O(n,

Polynomials for GLp×GLq orbit closures in the flag variety

\mathbb{C}

Combinatorial Results on (1, 2, 1, 2)-Avoiding GL(p, ℂ) × GL(q, ℂ)-Orbit Closures on GL(p+q, ℂ)/B

) or Sp(n,