Simply-laced Coxeter groups and groups generated by symplectic transvections

Details Simply-laced Coxeter groups and groups generated by symplectic transvections Simply-laced Coxeter groups and groups generated by symplectic transvections

1999-06-29

arxiv.org/abs/math/9906203v1

Mathematics

Algebraic Geometry

LaTeX, 18 pages, 4 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Simply-laced Coxeter groups and groups generated by symplectic transvections does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Simply-laced Coxeter groups and groups generated by symplectic transvections, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Simply-laced Coxeter groups and groups generated by symplectic transvections will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-422483