Lattice Paths, Young Tableaux, and Weight Multiplicities
Lattice Paths, Young Tableaux, and Weight Multiplicities
复制标题
格子路径、年轻画面和权重多重性
DOI：
10.1007/s00026-018-0374-4
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发表时间：
2015
影响因子：
0.5
通讯作者：
K. Misra
中科院分区：
文献类型：
--
作者：
R. Jayne;K. Misra
对于彩色方格，我们考虑了k−1格路径的若干可容许序列。我们证明了这种允许的格路径序列的个数由shapewith的标准Young表的个数的平方和给出，这也是在（k+ 1）k···21避免排列的个数。最后，我们将这一结果应用到仿射李代数的表示理论中，并证明了在不可约的最高权模中某些最大主导权的多重性。
Forand, we consider certain admissible sequences ofk−1 lattice paths in a coloredsquare. We show that the number of such admissible sequences of lattice paths is given by the sum of squares of the number of standard Young tableaux of shapewith, which is also the number of (k+ 1)k··· 21-avoiding permutations in. Finally, we apply this result to the representation theory of the affine Lie algebraand show that this gives the multiplicity of certain maximal dominant weights in the irreducible highest weight-module.
仿射李代数表示的最大权重的模式避免
影响因子：
1
作者：
Tomoaki Okayama and Shu Hanada;Shunsuke Tsuchioka and Masaki Watanabe
通讯作者：
Shunsuke Tsuchioka and Masaki Watanabe