ON GENERIC FLAG VARIETIES FOR ODD SPIN GROUPS

Abstract

For the spin group $G={\text{Spin}}_{2n+1}$ with arbitrary $n$, a generic $G$-torsor $E$ over a field, and a parabolic subgroup $P\subset G$, we consider the generic flag variety $E/P$ and describe its Chow ring modulo torsion. This description determines the index of $E/P$, completing results of [3], where the index has been determined for most $P$.