Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Calogero-Moser versus Kazhdan-Lusztig cells   In 1979, Kazhdan and Lusztig developed a combinatorial theory associated with
Coxeter groups. They defined in particular partitions of the group in left and
two-sided cells. In 1983, Lusztig generalized this theory to Hecke algebras of
Coxeter groups with unequal parameters. We propose a definition of left cells
and two-sided cells for complex reflection groups, based on ramification theory
for Calogero-Moser spaces. These spaces have been defined via rational
Cherednik algebras by Etingof and Ginzburg. We conjecture that these coincide
with Kazhdan-Lusztig cells, for real reflection groups. Counterparts of
families of irreducible characters have been studied by Gordon and Martino, and
we provide here a version of left cell representations. The Calogero-Moser
cells will be studied in details in a forthcoming paper, providing thus several
results supporting our conjecture.

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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th