Provides generators and relations for monoidal crystal categories of simple complex Lie algebras with explicit small-rank examples.
Growth Problems for Representations of Finite Monoids
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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.
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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.
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Presentations for categories of crystals
Provides generators and relations for monoidal crystal categories of simple complex Lie algebras with explicit small-rank examples.
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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.