Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Skew cellularity of the Hecke algebras of type $G(\ell,p,n)$   This paper introduces (graded) skew cellular algebras, which generalise
Graham and Lehrer's cellular algebras. We show that all of the main results
from the theory of cellular algebras extend to skew cellular algebras and we
develop a ``cellular algebra Clifford theory'' for the skew cellular algebras
that arise as fixed point subalgebras of cellular algebras.
  As an application of this general theory, the main result of this paper
proves that the Hecke algebras of type $G(\ell,p,n)$ are graded skew cellular
algebras. In the special case when $p = 2$ this implies that the Hecke algebras
of type $G(\ell,2,n)$ are graded cellular algebras. The proof of all of these
results rely, in a crucial way, on the diagrammatic Cherednik algebras of
Webster and Bowman. Our main theorem extends Geck's result that the one
parameter Iwahori-Hecke algebras are cellular algebras in two ways. First, our
result applies to all cyclotomic Hecke algebras in the infinite series in the
Shephard-Todd classification of complex reflection groups. Secondly, we lift
cellularity to the graded setting.
  As applications of our main theorem, we show that the graded decomposition
matrices of the Hecke algebras of type $G(\ell,p,n)$ are unitriangular, we
construct and classify their graded simple modules and we prove the existence
of ``adjustment matrices'' in positive characteristic.

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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: econ