Geometric induction for algebraic supergroups
Seminar Room 1, Newton Institute
Let G be a classical algebraic supergroup, and H be its subgroup. The geometric induction functor is the derived functor from the category of H-modules to the category of G-modules. It is defined as the cohomology of vector bundles on G/H. We study this functor in detail in case when H is a parabolic subgroup and G=SL(m,n) or OSP(m,2n) and use this result to find the characters of all irreducible representations of G.