2025/02/05 by David He, He, David, Daniel Tubbenhauer +1 · 3 citations
Computer Science · Mathematics · #18M05 #20M30 #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Primary: Primary: 11N45 #Representation Theory (math.RT) #Rings, Modules, and Algebras #Secondary: 20M20 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2502.02849
openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a conjecture for the asymptotic growth rate of the number of indecomposable summands in the tensor powers of representations of finite monoids, expressing it in terms of the (Brauer) character table of the monoid's group of units. We prove it under an additional hypothesis. We also give (exact and asymptotic) formulas for the growth rate of the length of the tensor powers when working over a good characteristic. As examples, we compute the growth rates for the full transformation monoid, the symmetric inverse monoid, and the monoid of 2 by 2 matrices. We also provide code used for our calculation.