Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules

Abstract Let {G} be a special parahoric group scheme of twisted type over the ring of formal power series over C, excluding the absolutely special case of A^ (2) ₂. Using the methods and results of Zhu, we prove a duality theorem for general {G}: there is a duality between the level one twisted affine Demazure modules and the function rings of certain torus fixed point subschemes in affine Schubert varieties for {G}. Along the way, we also establish the duality theorem for E₆. As a consequence, we determine the smooth locus of any affine Schubert variety in the affine Grassmannian of {G}. In particular, this confirms a conjecture of Haines and Richarz.