On the dual canonical and Kazhdan-Lusztig bases and 3412-, 4231-avoiding permutations
On the dual canonical and Kazhdan-Lusztig bases and 3412-, 4231-avoiding permutations
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DOI：
10.1016/j.jpaa.2007.09.007
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发表时间：
2008-05
影响因子：
0.8
通讯作者：
Marcos Skandera
中科院分区：
文献类型：
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作者：
Marcos Skandera
利用杜氏对坐标环O（GL（n，C））的对偶标准基的刻画，我们用内蕴式表示了该标准基的所有元素.然后我们给出了一个新的置换w的因式分解，避免了模式3412和4231，这反过来又产生了Hecke代数Hn（q）的相应Kazhdan-Lusztig基元Cw′（q）的因式分解。利用内禀函数和因式分解的结果，我们证明了对于每个完全非负的内禀函数Immf（x）及其关于Kazhdan-Lusztig内禀函数基的展开式∑dwImmw（x），当w避开模式3412和4231时，系数dw必须是非负的.
Using Du’s characterization of the dual canonical basis of the coordinate ring O(GL(n,C)), we express all elements of this basis in terms of immanants. We then give a new factorization of permutations w avoiding the patterns 3412 and 4231, which in turn yields a factorization of the corresponding Kazhdan–Lusztig basis elements Cw′(q) of the Hecke algebra Hn(q). Using the immanant and factorization results, we show that for every totally nonnegative immanant Immf(x) and its expansion ∑dwImmw(x) with respect to the basis of Kazhdan–Lusztig immanants, the coefficient dwmust be nonnegative when w avoids the patterns 3412 and 4231.