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

Abstract

Let $\mathcal{G}$ be a special parahoric group scheme of twisted type over the ring of formal power series over $\mathbb{C}$, excluding the absolutely special case of $A_{2\ell }^{(2)}$. Using the methods and results of Zhu, we prove a duality theorem for general $\mathcal{G}$ : 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 $\mathcal{G}$. Along the way, we also establish the duality theorem for $E_6$. As a consequence, we determine the smooth locus of any affine Schubert variety in the affine Grassmannian of $\mathcal{G}$. In particular, this confirms a conjecture of Haines and Richarz.

Accepted Journal version. With an appendix by Travis Scrimshaw. The SageMath code for the implementation in this appendix is included as an ancillary file

References in corpus (1)

• Beilinson-Drinfeld Schubert varieties of parahoric group schemes and twisted global Demazure modules