Equivariant K-theory of Grassmannians II: The Knutson-Vakil conjecture

TL;DR

This paper proves a corrected combinatorial puzzle rule for the equivariant K-theory of Grassmannians, confirming the Knutson-Vakil conjecture and linking it to existing tableau rules for Schubert calculus.

Contribution

It resolves the Knutson-Vakil conjecture by providing a corrected puzzle rule and connects it to a tableau rule for Schubert calculus.

Findings

Confirmed the corrected puzzle rule for equivariant K-theory of Grassmannians.

Linked puzzle rule to tableau rule for Schubert calculus.

Established a combinatorial connection between two approaches.

Abstract

In 2005, A. Knutson--R. Vakil conjectured a puzzle rule for equivariant K-theory of Grassmannians. We resolve this conjecture. After giving a correction, we establish a modified rule by combinatorially connecting it to the authors' recently proved tableau rule for the same Schubert calculus problem.