A new Littlewood-Richardson rule for Schur P-functions
A new Littlewood-Richardson rule for Schur P-functions
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Schur P 函数的新 Littlewood-Richardson 规则
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Soojin Cho
中科院分区：
文献类型：
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作者：
Soojin Cho
.利用L.最近提出的半标准分解图给出了移位Littlewood-Richardson系数的新描述。塞拉诺。我们还证明了半标准分解表集在Lascoux-Schüutzenberger对合作用下是不变的，从而提供了Schur P -函数对称性的一个组合证明.我们找到了L所作猜想的反例。塞拉诺关于斜Schur P -函数的猜想，证明了该猜想的错误性.半标准分解表的许多组合性质也显示。
. A new description of shifted Littlewood-Richardson coefficients is given in terms of semistandard decomposition tableaux which were recently introduced by L. Serrano. We also show that the set of semistandard decomposition tableaux is invariant under the action of Lascoux-Sch¨utzenberger involution, providing a combinatorial proof of the symmetry of Schur P -functions. We find counterexamples to the conjecture made by L. Serrano on skew Schur P -functions, proving the falsity of the conjecture. Many combinatorial properties of semistandard decomposition tableaux are also shown.