Vexillary degeneracy loci classes in K-theory and algebraic cobordism

TL;DR

This paper derives determinant formulas for the K-theory classes of vexillary degeneracy loci and extends these results to algebraic cobordism, providing new tools for understanding degeneracy loci in algebraic geometry.

Contribution

It introduces determinant formulas for vexillary degeneracy loci classes in K-theory and generalizes them to algebraic cobordism, advancing the computational methods in algebraic geometry.

Findings

Determinant formulas for K-theory classes of vexillary degeneracy loci.

Determinant formulas for double Grothendieck polynomials.

Extension of formulas to algebraic cobordism.

Abstract

In this paper, we prove determinant formulas for the $K$-theory classes of the structure sheaves of degeneracy loci classes associated to vexillary permutations in type $A$. As a consequence we obtain determinant formulas for Lascoux-Sch\"utzenberger's double Grothendieck polynomials associated to vexillary permutations. Furthermore, we generalize the determinant formula to algebraic cobordism.