R-matrices of U_qOSP(1,2) for highest weight representations of U_qOSP(1,2) for general q and q is an odd root of unity

TL;DR

This paper derives explicit R-matrices for the quantum superalgebra U_qOSP(1,2) across various representations, including highest weight modules, for general q and roots of unity, advancing understanding of its intertwining operators.

Contribution

It provides explicit formulas for the R-matrix of U_qOSP(1,2) for highest weight and other representations, including at roots of unity, which was previously not fully characterized.

Findings

Explicit R-matrix formulas for U_qOSP(1,2) Verma modules.

R-matrices for semiperiodic and spin representations.

Extension of R-matrix construction to roots of unity cases.

Abstract

We obtain the formula for intertwining operator(R-matrix) of quantum universal enveloping superalgebra U_qOSP(1,2) for U_qOSP(1,2)-Verma modules. By its restriction we obtain the R-matrix for two semiperiodic(semicyclic), two spin-j and spin-j and semiperiodic representations