The nonnegative part of quantum group \(U_q(\text{sl}(2))\) (Q2719911)

This article describes the centre and the finite dimensional irreducible representations of \(U_q^{\geq 0}\), the non-negative half part of the quantum group of \(\text{sl}_2\) (for \(q\) generic or a root of unity). These results are known in greater generality: for any semisimple Lie algebra the finite dimensional irreducible representations of the non-negative part of the corresponding quantum group (at a root of unity) are described by \textit{C. De Concini} and \textit{C. Procesi} [in Aust. Math. Soc. Lect. Ser. 9, 127-160 (1997; Zbl 0901.17005)] and its centre is determined by \textit{I. Gordon} [in ``Representations of semisimple Lie algebras in positive characteristic and quantum groups at roots of unity'', Lond. Math. Soc. Lect. Note Ser. 290, 149-167 (2001; Zbl 0980.00028)].