Generic modules over the quantum group \(U_t(sl(2))\) at \(t\) a root of unit
The author considers infinite dimensional modules of the quantum group \(U_t(sl(2))\) at \(t\) a \(4r\)-th root of unity. He gives a complete classification and an explicit construction of all generic \(U_ t(sl(2))\)-modules. Recall that a \(U_t(sl(2))\)-module \(M\) is called generic if \(M\) is indecomposable, \(M\) is infinite dimensional over \(\mathbb{Q}(t)\), but \(M\) is of finite length as \(\text{End}_{U_t(sl(2))}M\)-module. There are \(2(r-1)\) non-isomorphic generic modules, and the author gives in addition an explicit description of \(\text{End}_{U_t(sl(2))}M\) for these modules.
scientific article; zbMATH DE number 599665
scientific article