Triangle presentations and tilting modules for SL_2k+1

2020/05/14 by Corey Jones, Jones, Corey
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.2005.07172

All comments welcome!

arxiv created 2021/07/23 · arxiv updated 2021/07/27

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 A_n-1 (n≥3). From a type 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 \mathbbk with characteristic p≥ n-1 such that q ≡ 1 mod p. When \mathbbk is algebraically closed and n odd, this gives new fiber functors on the category of tilting modules for SL_n.

Related

• Infinite families of triangle presentations
• Quivers for SL(2) tilting modules
• Module categories for A_n web categories from A_n-1-buildings
• Triangle Presentations Encoded by Perfect Difference Sets
• Generalized tilting theory