Coxeter groups preserving orthants
Representation Theory
2024-12-30 v1
Abstract
In this short, elementary note we prove that if a faithful reflection representation of a Coxeter group preserves an orthant, then that Coxeter group is a product of symmetric groups acting on its natural permutation representation. We also prove an affine analogue of this statement, where an orthant is preserved modulo an invariant sublattice. As a consequence, the existence of two different versions of the quantum geometric Satake equivalence is a purely type A phenomenon.
Cite
@article{arxiv.2412.19749,
title = {Coxeter groups preserving orthants},
author = {Ben Elias},
journal= {arXiv preprint arXiv:2412.19749},
year = {2024}
}