Let G be a special parahoric group scheme of twisted type, excluding the absolutely special case for twisted A2n. 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 function rings of certain torus fixed point subschemes in twisted affine Schubert varieties for G. Along the way, we also establish the duality theorem for untwisted E6. As a consequence, we determine the smooth
locus of any affine Schubert variety in affine Grassmannian of G, which confirms a conjecture of Haines and Richarz.
This is joint work with Marc Besson.
This video was part of the Southeastern Lie Theory Workshop XII.
