Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
For any simple complex Lie algebra finite dimensional representations of its quantum \(t\)-analogue (a deformation of its universal enveloping algebra with parameter \(t\)) are proven to be completely reducible if t is not a root of 1. For the irreducible ones there is proven a highest weight theorem and, moreover, they are shown to be deformations of the representations of the initial enveloping algebra. For \(\text{sl}(2)\) the result matches that by \textit{A. V. Odesskii} [An analogue of the Sklyanin algebra, Funkts. Anal. Prilozh. 20, No. 2, 78--79 (1986; Zbl 0606.17013)].
scientific article; zbMATH DE number 4061458