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

Besson, Marc  ; Hong, Jiuzu 

Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e121

Résumé

Let ${\mathscr {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 $A^{(2)}_{2\ell }$. Using the methods and results of Zhu, we prove a duality theorem for general ${\mathscr {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 ${\mathscr {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 ${\mathscr {G}} $. In particular, this confirms a conjecture of Haines and Richarz.

Détail

DOI : 10.1017/fms.2025.10057

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