Conjecture expressing asymptotic growth of indecomposable summands in monoid-representation tensor powers via the Brauer character table of the group of units, with a proof under an extra hypothesis plus exact and asymptotic length formulas in good characteristic.
Asymptotics in infinite monoidal categories
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
We discuss formulas for the asymptotic growth rate of the number of summands in tensor powers in certain (finite or infinite) monoidal categories. Our focus is on monoidal categories with infinitely many indecomposable objects, with our main tools being generalized Perron-Frobenius theory alongside techniques from random walks.
fields
math.RT 2years
2025 2verdicts
UNVERDICTED 2representative citing papers
Derives asymptotic formulas for the growth rate of the number of summands in tensor powers of the generating object in semisimple diagram/interpolation categories.
citing papers explorer
-
Growth Problems for Representations of Finite Monoids
Conjecture expressing asymptotic growth of indecomposable summands in monoid-representation tensor powers via the Brauer character table of the group of units, with a proof under an extra hypothesis plus exact and asymptotic length formulas in good characteristic.
-
Growth problems in diagram categories
Derives asymptotic formulas for the growth rate of the number of summands in tensor powers of the generating object in semisimple diagram/interpolation categories.