Pieri rule for the affine flag variety
Copyright policy )Pieri rule for the affine flag variety
We prove the affine Pieri rule for the cohomology of the affine flag variety conjectured by Lam, Lapointe, Morse and Shimozono. We study the cap operator on the affine nilHecke ring that is motivated by Kostant and Kumar’s work on the equivariant cohomology of the affine flag variety. We show that the cap operators for Pieri elements are the same as Pieri operators defined by Berg, Saliola and Serrano. This establishes the affine Pieri rule. Nous prouvons la règle affine Pieri pour la cohomologie de la variété affine de drapeau conjecturé par Lam, Lapointe, Morse et Shimozono. Nous étudions l’opérateur de bouchon sur l’affine nilHecke anneau qui est motivé par le travail de Kostant et Kumar sur la cohomologie équivariante de la variété affine de drapeau. Nous montrons que les opérateurs de capitalisation pour les éléments Pieri sont les mêmes que les opérateurs Pieri définies par Berg, Saliola et Serrano. Ceci établit la règle affine Pieri.
- Korea Institute for Advanced Study Korea (Republic of)
Pieri rule, strong Schur function, Homogeneous spaces and generalizations, Classical problems, Schubert calculus, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], nilcoxeter algebra, $k$ -schur function, affine flag variety, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Mathematics - Algebraic Geometry, $k$ -Schur function, pieri rule, QA1-939, FOS: Mathematics, k-Schur function, Mathematics - Combinatorics, Combinatorics (math.CO), nilCoxeter algebra, Algebraic Geometry (math.AG), Mathematics, strong schur function
Pieri rule, strong Schur function, Homogeneous spaces and generalizations, Classical problems, Schubert calculus, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], nilcoxeter algebra, $k$ -schur function, affine flag variety, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Mathematics - Algebraic Geometry, $k$ -Schur function, pieri rule, QA1-939, FOS: Mathematics, k-Schur function, Mathematics - Combinatorics, Combinatorics (math.CO), nilCoxeter algebra, Algebraic Geometry (math.AG), Mathematics, strong schur function
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