2018/01/11 by Peter Fiebig, Fiebig, Peter, Martina Lanini +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1801.03959
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
openalex publication_date 2018/01/11 · arxiv created 2020/04/05 · arxiv updated 2020/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.