Resumen de Proof of a conjectured Möbius inversion formula for Grothendieck polynomials
Oliver Pechenik, Matthew Satriano
Schubert polynomials Ϭw are polynomial representatives for cohomology classes of Schubert varieties in a complete flag variety, while Grothendieck polynomials Ϭw are analogous representatives for the K-theory classes of the structure sheaves of Schubert varieties. In the special case that Ϭw is a multiplicity-free sum of monomials, K. Mészáros, L. Setiabrata, and A. St. Dizier conjectured that Ϭw can be easily computed from Sw via Möbius inversion on a certain poset. We prove this conjecture. Our approach is to realize monomials as Chow classes on a product of projective spaces and invoke a result of M. Brion on flat degenerations of such classes.
