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