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arXiv · 2001.06600

The Drinfeld stratification for ${\rm GL}_n$

Charlotte Chan·Alexander B. Ivanov
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Abstract

We define a stratification of Deligne--Lusztig varieties and their parahoric analogues which we call the Drinfeld stratification. In the setting of inner forms of GLn, we study the cohomology of these strata and give a complete description of the unique closed stratum. We state precise conjectures on the representation-theoretic behavior of the stratification. We expect this stratification to play a central role in the investigation of geometric constructions of representations of $p$-adic groups.

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Charlotte Chan, Alexander B. Ivanov. 2020-01-18. The Drinfeld stratification for ${\rm GL}_n$. https://arxiv.org/abs/2001.06600

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