On the structure of $End_{u_k(2)}(Ω_k^{\otimes r})$

Let $u_k(2)$ be the infinitesimal quantum $\frak{gl}_2$ over $k$, where $k$ is a field containing an $l$th primitive root $ε$ of 1 with $l\geq 3$ {\it odd}. We will determine the basic algebra for ${u_k(2)}(Ω_k^{\otimes r})$, where $Ω_k$ is the natural module for $u_k(2)$.

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