On the Canonical Representatives of a Finite Weyl Group
Abstract
Let K be a field and G a split connected reductive affine algebraic K-group. Let T be a split maximal torus of G, W its finite Weyl group, and R its root system. After fixing a realization of R in G and choosing a simple system for R, one gets a system of representatives for W in G(K), called the Canonical Representatives. It is well-known that these representatives rarely form a subgroup, and it is necessary for some questions to understand and quantify this failure. Various new formulas are given which constitute progress in this direction. An application of such formulas to the simple supercuspidals of Gross-Reeder and Reeder-Yu is provided.
Keywords
Cite
@article{arxiv.1505.07442,
title = {On the Canonical Representatives of a Finite Weyl Group},
author = {Sean Rostami},
journal= {arXiv preprint arXiv:1505.07442},
year = {2016}
}
Comments
substantial update/rewrite of previous version; 26 pages, standard formatting, no pictures; comments welcome