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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/4073

Title: Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions
Authors: Lapointe, L.
Morse, J.
Keywords: Affine Weyl group; Cores; k-Schur functions; Macdonald polynomials
Issue Date: 2005
Publisher: Elsevier Inc.
Citation: Journal of Combinatorial Theory, Series A 112 (1): 44-81
Abstract: The k-Young lattice Yk is a partial order on partitions with no part larger than k. This weak subposet of the Young lattice originated (Duke Math. J. 116 (2003) 103–146) from the study of the k-Schur functions , symmetric functions that form a natural basis of the space spanned by homogeneous functions indexed by k-bounded partitions. The chains in the k-Young lattice are induced by a Pieri-type rule experimentally satisfied by the k-Schur functions. Here, using a natural bijection between k-bounded partitions and k+1-cores, we establish an algorithm for identifying chains in the k-Young lattice with certain tableaux on k+1 cores. This algorithm reveals that the k-Young lattice is isomorphic to the weak order on the quotient of the affine symmetric group by a maximal parabolic subgroup. From this, the conjectured k-Pieri rule implies that the k-Kostka matrix connecting the homogeneous basis {hλ}λYk to may now be obtained by counting appropriate classes of tableaux on k+1-cores. This suggests that the conjecturally positive k-Schur expansion coefficients for Macdonald polynomials (reducing to q,t-Kostka polynomials for large k) could be described by a q,t-statistic on these tableaux, or equivalently on reduced words for affine permutations.
Description: Lapoint, L. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
URI: http://dspace.utalca.cl/handle/1950/4073
ISSN: 0097-3165
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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