Primitive vectors in induced supermodules for general linear supergroups

The purpose of the paper is to derive formulas that describe the structure of the induced supermodule HG0(λ) for the general linear supergroup G=GL(m|n)G=GL(m|n) over an algebraically closed field K   of characteristic p≠2p≠2. Using these formulas we determine primitive Gev=GL(m)×GL(n)Gev=GL(m)×GL(n)-vectors in HG0(λ). We conclude with remarks related to the linkage principle in positive characteristic.