Mirabolic Robinson-Schensted-Knuth correspondence
Mirabolic Robinson-Schensted-Knuth correspondence
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Mirabolic Robinson-Schensted-Knuth 对应关系
DOI：
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发表时间：
2008
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影响因子：
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通讯作者：
Roman Travkin
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文献类型：
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作者：
Roman Travkin
GL（V）在Fl（V）× Fl（V）× V中的轨道集是有限的，并且在所罗门的工作中用某些装饰置换集参数化.我们描述了一个Mirabolic RSK对应（双射）这一组的装饰排列和一组三元组：一对标准的杨tableaux，和一个额外的分区。它产生了一个分区的一套轨道组合细胞。我们证明了相同的划分是由一个轨道的一般余法向量的类型。我们猜想GL（V）的Iwahori-Hecke代数上由Fl（V）× Fl（V）×V生成的双模中的双模Kazhdan-Lusztig胞腔也给出了同样的划分.我们还给出了GL（V）× V上幂幺奇异特征层分类的理论应用。
The set of orbits of GL(V ) in F l(V ) × F l(V ) × V is finite, and is parametrized by the set of certain decorated permutations in a work of Solomon. We describe a Mirabolic RSK correspondence (bijective) between this set of decorated permutations and the set of triples: a pair of standard Young tableaux, and an extra partition. It gives rise to a partition of the set of orbits into combinatorial cells. We prove that the same partition is given by the type of a general conormal vector to an orbit. We conjecture that the same partition is given by the bimodule Kazhdan-Lusztig cells in the bimodule over the Iwahori-Hecke algebra of GL(V ) arising from F l(V )×F l(V )×V . We also give conjectural applications to the classification of unipotent mirabolic character sheaves on GL(V )× V .