Degeneracy locus formulas for amenable Weyl group elements

TL;DR

This paper introduces amenable Weyl group elements in types B, C, and D, generalizing vexillary permutations, and derives formulas for cohomology classes of degeneracy loci using flagged theta and eta polynomials.

Contribution

It defines amenable Weyl group elements in Lie types B, C, and D and links them to flagged theta and eta polynomials for degeneracy loci.

Findings

Defined amenable Weyl group elements in types B, C, D

Established formulas for cohomology classes of degeneracy loci

Connected flagged polynomials to geometric degeneracy loci

Abstract

We define a class of amenable Weyl group elements in the Lie types B, C, and D, which we propose as the analogues of vexillary permutations in these Lie types. Our amenable signed permutations index flagged theta and eta polynomials, which generalize the double theta and eta polynomials of Wilson and the author. In geometry, we obtain corresponding formulas for the cohomology classes of symplectic and orthogonal degeneracy loci.