K-theory of minuscule varieties

TL;DR

This paper establishes a new uniform Littlewood-Richardson rule for K-theoretic Schubert structure constants across all minuscule homogeneous spaces, simplifying calculations especially for Grassmannians and orthogonal Grassmannians.

Contribution

It introduces a novel, uniform combinatorial rule for K-theoretic structure constants that applies to all minuscule varieties, improving computational simplicity.

Findings

Provides a new combinatorial formula for K-theoretic structure constants

Simplifies calculations for Grassmannians and orthogonal Grassmannians

First uniform rule applicable to all minuscule homogeneous spaces

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.