论文标题
旋转表示的二元性
Dualities for spin representations
论文作者
论文摘要
令$ s $为$ u_q \ mathfrak {so} _n $的旋转器表示，对于$ n $奇数和$ q^2 $而不是团结。我们表明，其在$ s^{\ otimes n} $上的操作的委托人由非标准量子组$ u'_ { - q^2} \ mathfrak {so} _n $表示。对于$ n $，即使是$ s = s = s _+\ oplus s _- $也具有类似的语句，$ u'_q \ mathfrak {so} _n $的不可约的旋转式表示的直接总和，由$ u'_ _ { - q}} \ mathfrak a $ n $ n $ - $ u'_ { - q} \ mathfrak {so} _n $。类似的陈述也适用于融合张量类别的类别，$ q $是一个团结根。
Let $S$ be the spinor representation of $U_q\mathfrak{so}_N$, for $N$ odd and $q^2$ not a rooot of unity. We show that the commutant of its action on $S^{\otimes n}$ is given by a representation of the nonstandard quantum group $U'_{-q^2}\mathfrak{so}_n$. For $N$ even, an analogous statement also holds for $S=S_+\oplus S_-$ the direct sum of the irreducible spinor representations of $U'_q\mathfrak{so}_N$, with the commutant given by $U'_{-q}\mathfrak{o}_n$, a $\mathbb{Z}/2$-extension of $U'_{-q}\mathfrak{so}_n$. Similar statements also hold for fusion tensor categories with $q$ a root of unity.
