Structure of the tensor product of two simple modules of quantum $GL_2$

In this article, we consider the tensor product of two simple modules of quanum $GL_2$ over a field of characteristic $p\neq 0$. We show that it can be expressed as a direct sum of indecomposable twisted tilting modules. This problem has been studied by Henke and Doty [1] for $SL_2$ and also later on for $SL_3$ by S R Doty, Chris Bowman and Stuart Martin, ([7, 8]).