Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simply-laced Coxeter groups and groups generated by symplectic
  transvections   Let W be an arbitrary Coxeter group of simply-laced type (possibly infinite
but of finite rank), u,v be any two elements in W, and i be a reduced word (of
length m) for the pair (u,v) in the Coxeter group W\times W. We associate to i
a subgroup Gamma_i in GL_m(Z) generated by symplectic transvections. We prove
among other things that the subgroups corresponding to different reduced words
for the same pair (u,v) are conjugate to each other inside GL_m(Z). We also
generalize the enumeration result of the first three authors (see AG/9802093)
by showing that, under certain assumptions on u and v, the number of
Gamma_i(F_2)-orbits in F_2^m is equal to 3\times 2^s, where s is the number of
simple reflections that appear in a reduced decomposition for u or v and F_2 is
the two-element field.

1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys