
doi: 10.46298/dmtcs.2470
We provide a new description of the Pieri rule of the homology of the affine Grassmannian and an affineanalogue of the charge statistics in terms of bounded partitions. This makes it possible to extend the formulation ofthe Kostka–Foulkes polynomials in terms of solvable lattice models by Nakayashiki and Yamada to the affine setting. Nous proposons une nouvelle description de la règle de Pieri de l’homologie de la variété Grassmannienneaffine et un analogue affine de la statistique de charge en termes de partitions bornées . Il est ainsi possible d’étendreau cas affine la formulation due à Nakayashiki et Yamada des polynômes de Kostka–Foulkes en termes de modèlesde réseaux résolubles.
affine Schubert calculus, Pieri rule, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], $k$-schur functions, Charge statistic, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], pieri rule, charge statistic, energy function, QA1-939, $k$-Schur functions, affine schubert calculus, Mathematics
affine Schubert calculus, Pieri rule, [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], $k$-schur functions, Charge statistic, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], pieri rule, charge statistic, energy function, QA1-939, $k$-Schur functions, affine schubert calculus, Mathematics
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