# Triangle presentations and tilting modules for SL$_{2k+1}$

### Corey Jones

North Carolina State University, Raleigh, USA

## Abstract

Triangle presentations are combinatorial structures on finite projective geometries which characterize groups acting simply transitively on the vertices of a locally finite building of type $\tilde{A}_{n-1},\ (n \ge 3)$. From a type $\tilde{A}_{n-1}$ triangle presentation on a geometry of order $q$, we construct a fiber functor on the diagrammatic monoidal category Web(SL$^{-}_{n})$ over any field $\mathbb{k}$ with characteristic $p\ge n − 1$ such that $q \equiv 1\ mod\ p$. When $\mathbb{k}$ is algebraically closed and $n$ odd, this gives new fiber functors on the category of tilting modules for SL$_{n}$.

## Cite this article

Corey Jones, Triangle presentations and tilting modules for SL$_{2k+1}$. J. Comb. Algebra 5 (2021), no. 1, pp. 59–92

DOI 10.4171/JCA/50