Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parabolic Deligne-Lusztig varieties   Motivated by the Brou\'e conjecture on blocks with abelian defect groups for
finite reductive groups, we study "parabolic" Deligne-Lusztig varieties and
construct on those which occur in the Brou\'e conjecture an action of a braid
monoid, whose action on their $\ell$-adic cohomology will conjecturally factor
trough a cyclotomic Hecke algebra. In order to construct this action, we need
to enlarge the set of varieties we consider to varieties attached to a "ribbon
category"; this category has a {\em Garside family}, which plays an important
role in our constructions, so we devote the first part of our paper to the
necessary background on categories with Garside families.

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The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex