SOS-representation for the $SL(2,\mathbb C)$-invariant $R$-operator and Feynman diagrams

In the first part of the paper the basic facts about unitary seires representations of the group $SL(2,\mathbb C)$ and corresponding solutions to the Yang–Baxter equatins are given. In the second part we derive SOS-representation of the $R$-operator and prove the corresponding Yang–Baxter equation. Using Feynman diagrams we perform the calculation of the kernel of the R-operator in SOS-represetation. The expression for the kernel is presented in the form of Mellin–Barnes integral.