K-theoretic Schubert calculus for OG(n, 2n+1) and jeu de taquin for shifted increasing tableaux

摘要

We present a proof of a Littlewood-Richardson rule for the K-theory of odd orthogonal Grassmannians OG(n, 2n+1), as conjectured by Thomas-Yong (2009). Specifically, we prove that rectification using the jeu de taquin for increasing shifted tableaux introduced there, is well-defined and gives rise to an associative product. Recently, Buch-Ravikumar (2012) proved a Pieri rule for OG(n, 2n+1) that confirms a special case of the conjecture. Together, these results imply the aforementioned conjecture.