Branching algebras for the general linear Lie superalgebra

We develop an algebraic approach to the branching of representations of the general linear Lie superalgebra glp|q( C), by constructing certain super commutative algebras whose structure encodes the branching rules. Using this approach, we derive the branching rules for restricting any irreducible polynomial representation V of glp|q( C) to a regular subalgebra isomorphic to glr|s( C)⊕ glr'|s'( C), glr|s( C)₁( C)r'+s' or glr|s( C), with $r+r'=p$ and $s+s'=q$. In the case of glr|s( C)₁( C)r'+s' with $s=0$ or $s=1$ but general r, we also construct a basis for the space of glr|s( C) highest weight vectors in V; when $r=s=0$, the branching rule leads to explicit expressions for the weight multiplicities of V in terms of Kostka numbers.