论文标题
扭曲仿射舒伯特品种和扭曲的仿射模块模块的光滑轨迹
Smooth locus of twisted affine Schubert varieties and twisted affine Demazure modules
论文作者
论文摘要
令$ \ mathscr {g} $成为扭曲类型的特殊类型方案，上面是$ \ mathbb {c} $，不包括绝对特殊情况的$ a_ {2 \ ell}^{（2）} $。使用Zhu的方法和结果，我们证明了一般$ \ mathscr {g} $的二元定理：在Oxpine offine Nepazure模块的第一级扭曲的仿射模块与某些圆环固定点的功能环之间存在双重性，$ \ mathscr {g} $ affine schubert schubert varieties中的函数环。一路上，我们还为$ e_6 $建立了二元定理。结果，我们确定了$ \ mathscr {g} $的仿生草中的任何仿射舒伯特品种的平滑源。特别是，这证实了海恩斯和里奇尔斯的猜想。
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 $A_{2\ell}^{(2)}$. 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.
