Bumpless pipe dreams and alternating sign matrices

Understand

In their work on the infinite flag variety, Lam, Lee, and Shimozono (2018) introduced objects called bumpless pipe dreams and used them to give a formula for double Schubert polynomials.

• We extend this formula to the setting of K-theory, giving an expression for double Grothendieck polynomials as a sum over a larger class of bumpless pipe dreams.
• Our proof relies on techniques found in an unpublished manuscript of Lascoux (2002).
• Lascoux showed how to write double Grothendieck polynomials as a sum over alternating sign matrices.