Sheaves on the alcoves and modular representations I
Abstract
We consider the set of affine alcoves associated with a root system R as a topological space and consider a certain category S of sheaves of Z-modules on this space. Here Z is the structure algebra of the root system over a field k. To any wall reflection we associate a wall crossing functor on S. In the companion article "Sheaves on the alcoves and modular representations II" we prove that S encodes the simple rational characters of the connected, simply connected algebraic group with root system R over k, in the case that k is algebraically closed with characteristic above the Coxeter number.
Cite
@article{arxiv.1801.03959,
title = {Sheaves on the alcoves and modular representations I},
author = {Peter Fiebig and Martina Lanini},
journal= {arXiv preprint arXiv:1801.03959},
year = {2020}
}
Comments
30 pages. Typos corrected in version 2. This is the companion article to "Sheaves on the alcoves and modular representations II". Both articles replace our earlier submissions arXiv:1508.05579 and arXiv:1504.01699