K-theory of minuscule varieties

Abstract

Based on Thomas and Yong's K-theoretic jeu de taquin algorithm, we prove a uniform Littlewood-Richardson rule for the K-theoretic Schubert structure constants of all minuscule homogeneous spaces. Our formula is new in all types. For the main examples of Grassmannians of type A and maximal orthogonal Grassmannians it has the advantage that the tableaux to be counted can be recognized without reference to the jeu de taquin algorithm.

37 pages

References in corpus (3)

• The direct sum map on Grassmannians and jeu de taquin for increasing tableaux
• K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
• d-Complete Posets Generalize Young Diagrams for the Jeu de Taquin Property

Cited by in corpus (13)

• Resonance in orbits of plane partitions and increasing tableaux
• Genomic Tableaux
• A symplectic refinement of shifted Hecke insertion
• A Chevalley formula for the equivariant quantum K-theory of cominuscule varieties
• Poset edge densities, nearly reduced words, and barely set-valued tableaux
• Promotion of increasing tableaux: frames and homomesies
• Orbits of Plane Partitions of Exceptional Lie Type
• K-theoretic Poirier-Reutenauer bialgebra
• Linear compactness and combinatorial bialgebras
• Dynamics of plane partitions: Proof of the Cameron-Fon-Der-Flaass conjecture
• Minuscule analogues of the plane partition periodicity conjecture of Cameron and Fon-Der-Flaass
• Positivity of minuscule quantum K-theory
• K-Knuth Equivalence for Increasing Tableaux