Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On loop Deligne--Lusztig varieties of Coxeter-type for inner forms of
  ${\rm GL}_n$   For a reductive group $G$ over a local non-archimedean field $K$ one can
mimic the construction from the classical Deligne--Lusztig theory by using the
loop space functor. We study this construction in special the case that $G$ is
an inner form of ${\rm GL}_n$ and the loop Deligne--Lusztig variety is of
Coxeter type. After simplifying the proof of its representability, our main
result is that its $\ell$-adic cohomology realizes many irreducible
supercuspidal representations of $G$, notably almost all among those whose
L-parameter factors through an unramified elliptic maximal torus of $G$. This
gives a purely local, purely geometric and -- in a sense -- quite explicit way
to realize special cases of the local Langlands and Jacquet--Langlands
correspondences.

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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: eess