Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interval groups related to finite Coxeter groups I   We derive presentations of the interval groups related to all quasi-Coxeter
elements in the Coxeter group of type $D_n$. Type $D_n$ is the only infinite
family of finite Coxeter groups that admits proper quasi-Coxeter elements. The
presentations we obtain are over a set of generators in bijection with what we
call a Carter generating set, and the relations are those defined by the
related Carter diagram together with a twisted or a cycle commutator relator,
depending on whether the quasi-Coxeter element is a Coxeter element or not. The
proof is based on the description of two combinatorial techniques related to
the intervals of quasi-Coxeter elements.
  In a subsequent work [4], we complete our analysis to cover all the
exceptional cases of finite Coxeter groups, and establish that almost all the
interval groups related to proper quasi-Coxeter elements are not isomorphic to
the related Artin groups, hence establishing a new family of interval groups
with nice presentations. Alongside the proof of the main results, we establish
important properties related to the dual approach to Coxeter and Artin groups.

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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn