# Crystal interpretation of a formula on the branching rule of types $B_{n}$, $C_{n}$, and $D_{n}$.

@article{Hiroshima2016CrystalIO, title={Crystal interpretation of a formula on the branching rule of types \$B\_\{n\}\$, \$C\_\{n\}\$, and \$D\_\{n\}\$.}, author={Toya Hiroshima}, journal={arXiv: Quantum Algebra}, year={2016} }

The branching coefficients of the tensor product of finite-dimensional irreducible $U_{q}(\mathfrak{g})$-modules, where $\mathfrak{g}$ is $\mathfrak{so}(2n+1,\mathbb{C})$ ($B_{n}$-type), $\mathfrak{sp}(2n,\mathbb{C})$ ($C_{n}$-type), and $\mathfrak{so}(2n,\mathbb{C})$ ($D_{n}$-type), are expressed in terms of Littlewood-Richardson (LR) coefficients in the stable region. We give an interpretation of this relation by Kashiwara's crystal theory by providing an explicit surjection from the LR…

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