Proof of a conjectured Möbius inversion formula for Grothendieck polynomials

• Oliver Pechenik ^[1] ; Matthew Satriano ^[1]
  1. [1] University of Waterloo

     University of Waterloo

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024
• Idioma: inglés
• DOI: 10.1007/s00029-024-00973-z
• Enlaces
  • Texto completo
• Resumen

  • 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.

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