In this paper we first provide the proof of \(\hbox {SU}(2)\)Y-Map convergence. Then, by using \(\hbox {SU}(1,1)\) LQG simplicity constraints, we define \(\hbox {SU}(1,1)\)Y-Map from infinitely differentiable with a compact support functions on \(\hbox {SU}(1,1)\) to the functions (not necessarily square integrable) on \(\hbox {SL}(2,C)\), and prove its convergence as well.

中文翻译：

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SU（2）和SU（1,1）Y-环形量子引力图中的映射

在本文中，我们首先提供\（\ hbox {SU}（2）\）Y -Map收敛的证明。然后，通过使用\（\ hbox {SU}（1,1）\） LQG简单约束，我们定义\（\ hbox {SU}（1,1）\）Y -Map从无限可微，并具有紧凑的支持功能。\（\ hbox {SU}（1,1）\）到\（\ hbox {SL}（2，C）\）上的函数（不一定是平方可积），并证明其收敛性。