On the structure of ${\rm End}_{u_k(2)}(\Omega _k^{\otimes r})$ End uk(2)(Ωk⊗r)

Abstract

Let uk(2) be the infinitesimal quantum \documentclass[12pt]{minimal}\begin{document}$\mathfrak {gl}_2$\end{document}gl2 over k, where k is a field containing an lth primitive root ε of 1 with l ⩾ 3 odd. We will determine the basic algebra for \documentclass[12pt]{minimal}\begin{document}${\rm End}_{u_k(2)}(\Omega _k^{\otimes r})$\end{document} End uk(2)(Ωk⊗r), where Ωk is the natural module for uk(2).