Matrix-Ball Construction of affine Robinson–Schensted correspondence
Matrix-Ball Construction of affine Robinson–Schensted correspondence
复制标题
仿射 Robinson-Schensted 对应关系的矩阵球构造
DOI：
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发表时间：
2015
影响因子：
0.7
通讯作者：
E. Yudovina
中科院分区：
文献类型：
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作者：
Michael Chmutov;P. Pylyavskyy;E. Yudovina
在他的研究Kazhdan-Lusztig细胞在仿射型A，施介绍了一个仿射模拟罗宾逊-申斯特对应。我们推广了Viennot和富尔顿的矩阵球构造，给出了Shi算法的一个更组合的实现。作为一个副产品，我们也给出了一种方法来实现仿射对应，通过通常的罗宾逊-申斯特碰撞算法。接下来，受Lusztig和Xi的启发，我们将算法扩展到扩展仿射对称群和三元组集合$$（P，Q，\rho）$$（P，Q，ρ）之间的双射，其中P和Q是小报，$$\rho $$ρ是主导权重。权重$\rho $$ρ在仿射矩阵球构造方面得到自然的解释。最后，我们证明了逆映射的纤维具有Weyl群对称性，解释了权的优势条件。
In his study of Kazhdan–Lusztig cells in affine type A, Shi has introduced an affine analog of Robinson–Schensted correspondence. We generalize the Matrix-Ball Construction of Viennot and Fulton to give a more combinatorial realization of Shi’s algorithm. As a byproduct, we also give a way to realize the affine correspondence via the usual Robinson–Schensted bumping algorithm. Next, inspired by Lusztig and Xi, we extend the algorithm to a bijection between the extended affine symmetric group and collection of triples $$(P, Q, \rho )$$(P,Q,ρ) where P and Q are tabloids and $$\rho $$ρ is a dominant weight. The weights $$\rho $$ρ get a natural interpretation in terms of the Affine Matrix-Ball Construction. Finally, we prove that fibers of the inverse map possess a Weyl group symmetry, explaining the dominance condition on weights.