2022/11/28 by Nate Harman, Harman, Nate, Andrew Snowden +3 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2211.15392
openalex publication_date 2022/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be the group of all order-preserving self-maps of the real line. In previous work, the first two authors constructed a pre-Tannakian category \underlineRep(G) associated to G. The present paper is a detailed study of this category, which we name the Delannoy category. We classify the simple objects, determine branching rules to open subgroups, and give a combinatorial rule for tensor products. The Delannoy category has some remarkable features: it is semi-simple in all characteristics; all simples have categorical dimension ± 1; and the Adams operations on its Grothendieck group are trivial. We also give a combinatorial model for \underlineRep(G) based on Delannoy paths.