Affineness of some quotient dur sheaves of a super affine group

Abstract

We prove that given a super affine closed subgroup $H$ of a super affine group $G$ over a field $k$ of charctersitic $\mathrm{ch} k \ne 2$, the dur $k$-sheaf $G\tilde{\tilde{/}} H$ of right cosets is affine if the affine $k$-group $\bar{H}$ assocoiated to $H$ is (a) reductive or (b) pro-finite. Especially when $G$ is algebraic, the result in Case (a) gives rise to a positive answer to Brundan's question which was recently discussed by Zubkov \cite{Z}.