We consider the Newton stratification on Iwahori-double cosets in the loop group of a reductive group. We describe a group-theoretic condition on the generic Newton point, called cordiality, under which the Newton poset (that is, the index set for non-empty Newton strata) is saturated and Grothendieck’s conjecture on closures of the Newton strata holds. Finally, we give several large classes of Iwahori-double cosets for which this condition is satisfied by studying certain paths in the associated quantum Bruhat graph.

中文翻译：

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Iwahori-double cosets 中的通用牛顿点和牛顿偏序

我们考虑还原群的环群中岩堀双陪集上的牛顿分层。我们描述了通用牛顿点上的群论条件，称为亲切，在该条件下，牛顿偏序（即非空牛顿地层的索引集）是饱和的，格洛腾迪克关于牛顿地层闭合的猜想成立。最后，我们通过研究相关的量子布鲁哈特图中的某些路径，给出了几个大类的 Iwahori 双陪集，它们满足了这个条件。