Semisimplifications and representations of the General Linear Supergroup

We study the semisimplification of the full karoubian subcategory generated by the irreducible finite dimensional representations of the algebraic supergroup $GL(m\mathrm{\mid }n)$ over an algebraically closed field of characteristic zero. This semisimplification is equivalent to the representations of a pro-reductive group $H_{m\mathrm{\mid }n}$. We show that there is a canonical decomposition $H_{m\mathrm{\mid }n}\cong GL(m\text{\hspace{0.17em}⁣}-\text{\hspace{0.17em}⁣}n)\times H_{n\mathrm{\mid }n}$, thereby reducing the determination of $H_{m\mathrm{\mid }n}$ to the equal rank case $m\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}n$ which was treated in a previous paper.