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

Clifford, Edward; Thomas, Hugh et Yong, Alexander (2014). « K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux ». Journal für die reine und angewandte Mathematik (Crelles Journal), 2014(690), pp. 51-63.

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Résumé

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.

Type: Article de revue scientifique
Mots-clés ou Sujets: Algebraic geometry, Projective and enumerative geometry, Classical problems, Schubert calculus; Combinatorics, Algebraic combinatorics, Combinatorial aspects of representation theory
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Hugh R. Thomas
Date de dépôt: 18 mai 2016 19:49
Dernière modification: 30 mai 2016 20:13
Adresse URL : http://www.archipel.uqam.ca/id/eprint/8484

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