Ribbon tableaux, Hall–Littlewood functions, quantum affine algebras, and unipotent varieties
Ribbon tableaux, Hall–Littlewood functions, quantum affine algebras, and unipotent varieties
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DOI：
10.1063/1.531807
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发表时间：
1995-12
影响因子：
1.3
通讯作者：
A. Lascoux;B. Leclerc;J. Thibon
中科院分区：
文献类型：
--
作者：
A. Lascoux;B. Leclerc;J. Thibon
我们引入了一种新的对称函数族，它是舒尔函数的乘积的q个类似物，定义为带状表。这些函数可以用Fock空间表示Fq （Uq(sln)）来解释，并通过旗子变体的几何关系与Hall-Littlewood函数联系起来。我们提出了一系列的猜想，并在特殊情况下证明了它们。证明这些函数实际上是对称的关键步骤包括使用带状表来计算Fq的最高权重向量的基础。
We introduce a new family of symmetric functions, which are q analogs of products of Schur functions, defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock space representation Fq of Uq(sln), and are related to Hall–Littlewood functions via the geometry of flag varieties. We present a series of conjectures, and prove them in special cases. The essential step in proving that these functions are actually symmetric consists in the calculation of a basis of highest weight vectors of Fq using ribbon tableaux.