Two Murnaghan-Nakayama rules in Schubert calculus

TL;DR

This paper extends the Murnaghan-Nakayama rule to Schubert polynomials and quantum cohomology, enabling new calculations of intersections in algebraic geometry.

Contribution

It introduces novel Murnaghan-Nakayama rules for Schubert polynomials and quantum cohomology, broadening computational tools in Schubert calculus.

Findings

Derived a Murnaghan-Nakayama rule for Schubert polynomials

Established a version for quantum cohomology of Grassmannians

Facilitated intersection calculations of Schubert cycles with tautological classes

Abstract

The Murnaghan-Nakayama rule expresses the product of a Schur function with a Newton power sum in the basis of Schur functions. We establish a version of the Murnaghan-Nakayama rule for Schubert polynomials and a version for the quantum cohomology ring of the Grassmannian. These rules compute all intersections of Schubert cycles with tautological classes coming from the Chern character.