Frobenius Kernels of Algebraic Supergroups and Steinberg’s Tensor Product Theorem

Abstract

AbstractFor a split quasireductive supergroup $$\mathbbm {G}$$ G defined over a field, we study structure and representation of Frobenius kernels $$\mathbbm {G}_r$$ G r of $$\mathbbm {G}$$ G and we give a necessary and sufficient condition for $$\mathbbm {G}_r$$ G r to be unimodular in terms of the root system of $$\mathbbm {G}$$ G . We also establish Steinberg’s tensor product theorem for $$\mathbbm {G}$$ G under some natural assumptions.