Vexillary degeneracy loci classes in [formula omitted]-theory and algebraic cobordism

Abstract

In this paper, we prove determinantal formulas for the K-theory classes of the structure sheaves of degeneracy loci associated to vexillary permutations in type A. As a consequence we obtain determinantal formulas for Lascoux–Schützenberger’s double Grothendieck polynomials associated to vexillary permutations. We also prove a generalization of the formula in algebraic cobordism.