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

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

2010-02-08

arxiv.org/abs/1002.1664v2

Mathematics

Combinatorics

13 pages; v2 has coauthor added

Scientific paper

We present a proof of a Littlewood-Richardson rule for the K-theory of odd orthogonal Grassmannians OG(n,2n+1), as conjectured in [Thomas-Yong '09]. 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 '09] proved a Pieri rule for OG(n,2n+1) that [Feigenbaum-Sergel '09] showed confirms a special case of the conjecture. Together, these results imply the aforementioned conjecture.

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