An approach to the branching rule from sl2n(C) to sp2n(C) via Littelmann's path model
An approach to the branching rule from sl2n(C) to sp2n(C) via Littelmann's path model
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DOI：
10.1016/j.jalgebra.2004.12.014
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发表时间：
2005-04
影响因子：
0.9
通讯作者：
S. Naito;Daisuke Sagaki
中科院分区：
文献类型：
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作者：
S. Naito;Daisuke Sagaki
我们提出了一个猜想，描述了从特殊线性李代数sl2n（C）（A2n−1型）到嵌入为sl2n（C）的图自同构的不动点子代数的辛李代数（Cn型）的分支规则。此外，我们在一定的情况下证明了猜想，并提供了一些支持的例子。此外，我们表明，分支系数可以得到明确通过使用逆Kostka矩阵和路径模型的定义（或自然）表示C2n的sl 2n（C）的对称功率的张量积。
We propose a conjecture describing the branching rule, in terms of Littelmann's path model, from the special linear Lie algebra sl2n(C) (of type A2n−1) to the symplectic Lie algebra (of type Cn) embedded as the fixed point subalgebra of the diagram automorphism of sl2n(C). Moreover, we prove the conjecture in certain cases, and also provide some supporting examples. In addition, we show that the branching coefficients can be obtained explicitly by using the inverse Kostka matrix and path models for tensor products of symmetric powers of the defining (or natural) representation C2nof sl2n(C).