Schubert Polynomials in Types A and C

Abstract

Enriched versions of type A Schubert polynomials are constructed with coefficients in a polynomial ring in variables $c_1,c_2,\dots$. Specializing these variables to $0$ recovers the double Schubert polynomials of Lascoux and Schützenberger; specializing them to certain power series recovers the back-stable double Schubert polynomials of Lam, Lee, and Shimozono; specializing them to Schur Q-polynomials relates them to the type C double Schubert polynomials of Ikeda, Mihalcea, and Naruse. Many formulas for classical Schubert polynomials generalize to this setting. They give, and are characterized by, formulas for degeneracy loci.

arXiv comment30 pages

References in corpus (2)

• Chern class formulas for classical-type degeneracy loci
• Identities for Schur-type determinants and pfaffians

Cited by in corpus (4)

• Back stable K-theory Schubert calculus
• Identities for Schur-type determinants and pfaffians
• Infinite flags and Schubert polynomials
• Shifted edge labeled tableaux and localizations