Degeneracy locus formulas for amenable Weyl group elements

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.

42 pages, 1 figure. Minor corrections and improvements made to the exposition; final version

References in corpus (7)

• Quantum Pieri rules for isotropic Grassmannians
• Double Schubert polynomials for the classical groups
• Chern class formulas for classical-type degeneracy loci
• A Giambelli formula for isotropic Grassmannians
• Degeneracy Loci, Pfaffians, and Vexillary Signed Permutations in Types B, C, and D
• Double theta polynomials and equivariant Giambelli formulas
• Double eta polynomials and equivariant Giambelli formulas