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arXiv · 2402.13216

Basic Loci of Positive Coxeter Type for $GL_n$

Ryosuke Shimada
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Abstract

Motivated by the problem of giving an explicit description of the basic locus in the reduction of Shimura varieties, G\"{o}rtz, He and Nie studied the cases where the basic affine Deligne-Lusztig variety, which serves as its group-theoretic model, is a union of classical Deligne-Lusztig varieties associated to Coxeter elements. In this paper, we study a natural generalization of this stratification in the case of $GL_n$.

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Ryosuke Shimada. 2024-02-20. Basic Loci of Positive Coxeter Type for $GL_n$. https://arxiv.org/abs/2402.13216

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