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

Abstract

Abstract. We present a proof of a Littlewood–Richardson rule for the K -theory of odd orthogonal Grassmannians OG( n ,2 n +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 ,2 n +1) that confirms a special case of the conjecture. Together, these results imply the aforementioned conjecture.

Locations

• Archipelago (Université du Québec à Montréal) - View - PDF
• Journal für die reine und angewandte Mathematik (Crelles Journal) - View