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arXiv · 1802.02456

Ordinary $GL_2(F)$-representations in characteristic two via affine Deligne-Lusztig constructions

Alexander B. Ivanov
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Abstract

The group $\GL_2$ over a local field with (residue) characteristic $2$ possesses much more smooth supercuspidal $\ell$-adic representations, than over a local field of residue characteristic $> 2$. One way to construct these representations is via the theory of types of Bushnell-Kutzko. We construct many of them in the cohomology of certain extended affine Deligne-Lusztig varieties attached to $\GL_2$ and wildly ramified maximal tori in it. Then we compare our construction with the type-theoretic one. The corresponding extended affine Deligne-Lusztig varieties were introduced in a preceding article. Also in the present case they turn out to be zero-dimensional.

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Alexander B. Ivanov. 2018-02-07. Ordinary $GL_2(F)$-representations in characteristic two via affine Deligne-Lusztig constructions. https://arxiv.org/abs/1802.02456

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