论文标题
偏僻的高几何功能和超对称6J符号
A parafermionic hypergeometric function and supersymmetric 6j-symbols
论文作者
论文摘要
我们研究双曲线超几何函数的偏fermionic概括是Liouville场理论的融合矩阵中最重要的部分，而Faddeev模块化双重双重的RACAH-WIGNER符号。我们表明，这种广义的超几何函数是稀有椭圆高几何函数$ v^{（r）} $的限制形式，并得出其转换属性和由其满足的混合差异方程。在中间级别，我们描述了更一般的稀有双曲超单几何函数的对称性。一个重要的$ r = 2 $案例对应于$ n = 1 $ super liouville field理论的融合矩阵中给出的超对称超测量功能，而量子代数$ {\ rm u} _q（{\ rm osp}（\ rm osp}（\ rm osp}（\ rm osp}（\ rm osp}（1 | 2），我们指出与标准regge对称性的关系，并通过建立不同的参数化来证明超对称RACAH-WIGNER符号的一些先前的猜想。
We study properties of a parafermionic generalization of the hyperbolic hypergeometric function appearing as the most important part in the fusion matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev modular double. We show that this generalized hypergeometric function is a limiting form of the rarefied elliptic hypergeometric function $V^{(r)}$ and derive its transformation properties and a mixed difference-recurrence equation satisfied by it. At the intermediate level we describe symmetries of a more general rarefied hyperbolic hypergeometric function. An important $r=2$ case corresponds to the supersymmetric hypergeometric function given by the integral appearing in the fusion matrix of $N=1$ super Liouville field theory and the Racah-Wigner symbols of the quantum algebra ${\rm U}_q({\rm osp}(1|2))$. We indicate relations to the standard Regge symmetry and prove some previous conjectures for the supersymmetric Racah-Wigner symbols by establishing their different parametrizations.
