Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On non-conjugate Coxeter elements in well-generated reflection groups   Given an irreducible well-generated complex reflection group W with Coxeter
number h, we call a Coxeter element any regular element (in the sense of
Springer) of order h in W; this is a slight extension of the most common notion
of Coxeter element. We show that the class of these Coxeter elements forms a
single orbit in W under the action of reflection automorphisms. For Coxeter and
Shephard groups, this implies that an element c is a Coxeter element if and
only if there exists a simple system S of reflections such that c is the
product of the generators in S. We moreover deduce multiple further
implications of this property. In particular, we obtain that all noncrossing
partition lattices of W associated to different Coxeter elements are
isomorphic. We also prove that there is a simply transitive action of the
Galois group of the field of definition of W on the set of conjugacy classes of
Coxeter elements. Finally, we extend several of these properties to Springer's
regular elements of arbitrary order.

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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: eess