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

Edward Clifford, Hugh Thomas and Alexander Yong

Abstract.

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.

Funding source: NSERC Discovery

Funding source: NSF

Award Identifier / Grant number: DMS-0601010

Funding source: NSF

Award Identifier / Grant number: DMS-0901331

We thank Anders Buch for informing us of [J. reine angew. Math. 668 (2012), 109–132] and the work of Feigenbaum and Sergel. We also thank Allen Knutson for a helpful communication concerning dual Schubert bases in K-theory. We thank the referee for suggestions which improved the clarity of the exposition.