Title: Tannakian duality for affine homogeneous spaces,
Abstract: Associated to any closed quantum subgroup $G\subset U_N^+$ and any index set
$I\subset\{1,\ldots,N\}$ is a certain homogeneous space $X_{G,I}\subset
S^{N-1}_{\mathbb C,+}$, called affine homogeneous space. We discuss here the
abstract axiomatization of the algebraic manifolds $X\subset S^{N-1}_{\mathbb
C,+}$ which can appear in this way, by using Tannakian duality methods.