Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cells in Coxeter groups I   The purpose of this article is to shed new light on the combinatorial
structure of Kazhdan-Lusztig cells in infinite Coxeter groups $W$. Our main
focus is the set $\D$ of distinguished involutions in $W$, which was introduced
by Lusztig in one of his first papers on cells in affine Weyl groups. We
conjecture that the set $\D$ has a simple recursive structure and can be
enumerated algorithmically starting from the distinguished involutions of
finite Coxeter groups. Moreover, to each element of $\D$ we assign an
explicitly defined set of equivalence relations on $W$ that altogether
conjecturally determine the partition of $W$ into left (right) cells. We are
able to prove these conjectures only in a special case, but even from these
partial results we can deduce some interesting corollaries.

9
The categories of this paper are: nlin
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph