Tableaux on k + 1-crores, reduced words for affine permutations, and k -Schur expansions

作者: Luc Lapointe , Jennifer Morse

DOI: 10.1016/J.JCTA.2005.01.003

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摘要: The k-Young lattice Yk is a partial order on partitons with no part larger than k. This weak subposet of the Young originated (Duke Math. J. 116 (2003) 103-146) from study k-Schur functions sλ(k), Symmetric that natural basis space spanned by homogeneous funtions indexed k-bounded partitions. chains in are induced Pieritype rule experimentally satisfied functions. Here, using bijection between and k + 1-cores, we establish an algorithm for identifying k- certain tableaux 1 cores. reveals isomorphic to quotient affine symmetric gruop S˜k+1 maximal parabolic subgruop. From this, conjectured k-Pieri implies k-Kostka matrix connecting {hλ}λ∈Yk {sλ(k)}λ∈Yk may now be obtained counting appropriate classes 1-cores. suggests conjecturally positive expansion coefficients Macdonald polynomials (reducing q, t-Kostka large k) could described t-statistic these tableaux, or equivalently reduced words permutations.

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