Primitive vectors in induced supermodules for general linear supergroups

Abstract

The purpose of the paper is to derive formulas that describe the structure of the induced supermodule H^0_G(\la) for the general linear supergroup G=GL(m|n) over an algebraically closed field K of characteristic p\neq 2. Using these formulas we determine primitive G_{ev}=GL(m)\times GL(n)-vectors in H^0_G(\lambda). We conclude with remarks related to the linkage principle in positive characteristic.