Equivariant K-theory of Grassmannians

Abstract

We address a unification of the Schubert calculus problems solved by [A. Buch '02] and [A. Knutson-T. Tao '03]. That is, we prove a combinatorial rule for the structure coefficients in the torus-equivariant K-theory of Grassmannians with respect to the basis of Schubert structure sheaves. We thereby deduce the conjectural rule of [H. Thomas-A. Yong '13] for the same coefficients. Both rules are positive in the sense of [D. Anderson-S. Griffeth-E. Miller '11] (and moreover in a stronger form). Our work is based on the combinatorics of genomic tableaux and a generalization of [M.-P. Schutzenberger '77]'s jeu de taquin.

93 pages

References in corpus (4)

• Genomic Tableaux
• Puzzles, positroid varieties, and equivariant K-theory of Grassmannians
• Equivariant K-theory of Grassmannians II: The Knutson-Vakil conjecture
• Monodromy and K-theory of Schubert curves via generalized jeu de taquin

Cited by in corpus (10)

• Resonance in orbits of plane partitions and increasing tableaux
• Genomic Tableaux
• Skew hook formula for $d$-complete posets
• A Chevalley formula for the equivariant quantum K-theory of cominuscule varieties
• A web basis of invariant polynomials from noncrossing partitions
• Crystal structures for symmetric Grothendieck polynomials
• The genomic Schur function is fundamental-positive
• Unique rectification in $d$-complete posets: towards the $K$-theory of Kac-Moody flag varieties
• Equivariant K-theory classes of matrix orbit closures
• Bumpless pipe dreams meet Puzzles