A statistic on the roots of a finite reflection group and a correspondence between the height function and Bruhat order
Combinatorics
2008-03-13 v4 Group Theory
Abstract
The action of a finite reflection group (type A) on its set of roots is understood as a permutation representation or group action. We show that this representation is an induced representation from a certain kind of parabolic subgroup. Furthermore, we use this representation to define a statistic (derived from the length function) on the set of roots. A possible application to Costas Arrays is hinted at in a proposition.
Keywords
Cite
@article{arxiv.0803.0782,
title = {A statistic on the roots of a finite reflection group and a correspondence between the height function and Bruhat order},
author = {Mark Sterling},
journal= {arXiv preprint arXiv:0803.0782},
year = {2008}
}