On computing the eventual behavior of an FI-module over the rational numbers
John D. Wiltshire-Gordon
TL;DR
This paper provides a formula to determine the long-term behavior of irreducible representations in finitely-presented FI-modules over the rationals, based on existing structure theory.
Contribution
It introduces a formula for the eventual multiplicities in FI-modules over the rationals, extending the understanding of their asymptotic representation behavior.
Findings
Derived a formula for multiplicities in FI-modules
Utilized structure theory from Sam-Snowden SS16
Enhanced understanding of asymptotic representation behavior
Abstract
We give a formula for the eventual multiplicities of irreducible representations appearing in a finitely-presented FI-module over the rational numbers. The result relies on structure theory due to Sam-Snowden SS16.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models