Translation and cancellation of socle series patterns (Q1118036)

Let G be a semi simple algebraic group over a field of prime characteristic and let \(G_ n\) denote the nth Frobenius kernel in G. Also let B be a Borel subgroup. The authors study the relations between induction from B to \(G_ nB\) and induction from B to G. Their main theorem says that for certain 1-dimensional B-modules \(\lambda\), the socle series of \(Ind^ G_ B\lambda\) may be obtained by applying \(Ind^ G_{G_ nB}\) to the \(G_ n\)-socle series of \(Ind_{G_ n}^{G_ nB}\lambda\). This is a generalization of a theorem by the reviewer [see Math. Z. 194, 127-142 (1987; Zbl 0595.20038)].