标题： 2-齐次二分距离正则图与量子群 $U^\prime_q(\mathfrak{so}_6)$ 显示英文标题

标题： 2-Homogeneous bipartite distance-regular graphs and the quantum group $U^\prime_q(\mathfrak{so}_6)$

摘要： 我们考虑一个直径为$D \geq 3$的2-齐次双部距离正则图$\Gamma$。我们假设$\Gamma$不是超立方体也不是圈。我们固定了$\Gamma$的本原幂等元的一种$Q$-多项式排序。这种$Q$-多项式排序由一个非零参数$q \in \mathbb C$描述，且该参数不是单位根。 我们利用一个$S_3$-对称的方法来研究$\Gamma$。 在这种方法中，考虑$V^{\otimes 3} = V \otimes V \otimes V$，其中$V$是$\Gamma$的标准模。 We construct a subspace $\Lambda$ of $V^{\otimes 3}$ that has dimension $\binom{D+3}{3}$, together with six linear maps from $\Lambda$ to $\Lambda$. Using these maps we turn $\Lambda$ into an irreducible module for the nonstandard quantum group $U^\prime_q(\mathfrak{so}_6)$ introduced by Gavrilik and Klimyk in 1991. 显示英文摘要

摘要： We consider a 2-homogeneous bipartite distance-regular graph $\Gamma$ with diameter $D \geq 3$. We assume that $\Gamma$ is not a hypercube nor a cycle. We fix a $Q$-polynomial ordering of the primitive idempotents of $\Gamma$. This $Q$-polynomial ordering is described using a nonzero parameter $q \in \mathbb C$ that is not a root of unity. We investigate $\Gamma$ using an $S_3$-symmetric approach. In this approach one considers $V^{\otimes 3} = V \otimes V \otimes V$ where $V$ is the standard module of $\Gamma$. We construct a subspace $\Lambda$ of $V^{\otimes 3}$ that has dimension $\binom{D+3}{3}$, together with six linear maps from $\Lambda$ to $\Lambda$. Using these maps we turn $\Lambda$ into an irreducible module for the nonstandard quantum group $U^\prime_q(\mathfrak{so}_6)$ introduced by Gavrilik and Klimyk in 1991.