论文标题
Coxeter Group的免费量子类似物$ D_4 $
Free quantum analogue of Coxeter group $D_4$
论文作者
论文摘要
我们定义了量子组$ d_4^+$ - 脱二光的免费量子版本$ d_4 $（coxeter系列$ d $的最小代表）。为了这样做，我们构建了一个免费的属性类似物，即$ 4 \ times4 $矩阵具有决定性属性。通常，这种决定因素的类似物通常很难定义自由量子组，而我们的结果仅适用于矩阵尺寸$ n = 4 $。然后，通过在免费的HyperoctaHeDral组$ H_4^+$上施加这种广义的决定因素来定义免费的$ d_4^+$。此外，我们给出了$ d_4^+$的表示类别的详细组合描述。
We define the quantum group $D_4^+$ -- a free quantum version of the demihyperoctahedral group $D_4$ (the smallest representative of the Coxeter series $D$). In order to do so, we construct a free analogue of the property that a $4\times4$ matrix has determinant one. Such analogues of determinants are usually very hard to define for free quantum groups in general and our result only holds for the matrix size $N=4$. The free $D_4^+$ is then defined by imposing this generalized determinant condition on the free hyperoctahedral group $H_4^+$. Moreover, we give a detailed combinatorial description of the representation category of $D_4^+$.
