TY - JOUR
T1 - K-theoretic Schubert calculus for OG(n, 2n + 1) and jeu de taquin for shifted increasing tableaux
AU - Clifford, Edward
AU - Thomas, Hugh
AU - Yong, Alexander
N1 - Funding Information:
Hugh Thomas is supported by an NSERC Discovery grant. Alexander Yong is partially supported by NSF grants DMS-0601010 and DMS-0901331.
PY - 2014/5
Y1 - 2014/5
N2 - 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.
AB - 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.
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U2 - 10.1515/crelle-2012-0071
DO - 10.1515/crelle-2012-0071
M3 - Article
AN - SCOPUS:84901743146
SN - 0075-4102
SP - 51
EP - 63
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 690
ER -