JournalsjcaVol. 5, No. 1pp. 59–92

Triangle presentations and tilting modules for SL2k+1_{2k+1}

  • Corey Jones

    North Carolina State University, Raleigh, USA
Triangle presentations and tilting modules for SL$_{2k+1}$ cover
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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~n1, (n3)\tilde{A}_{n-1},\ (n \ge 3). From a type A~n1\tilde{A}_{n-1} triangle presentation on a geometry of order qq, we construct a fiber functor on the diagrammatic monoidal category Web(SLn)^{-}_{n}) over any field k\mathbb{k} with characteristic pn1p\ge n − 1 such that q1 mod pq \equiv 1\ mod\ p. When k\mathbb{k} is algebraically closed and nn odd, this gives new fiber functors on the category of tilting modules for SLn_{n}.

Cite this article

Corey Jones, Triangle presentations and tilting modules for SL2k+1_{2k+1}. J. Comb. Algebra 5 (2021), no. 1, pp. 59–92

DOI 10.4171/JCA/50