Computations of Stable Multiplicities in the Cohomology of Configuration Space

Computations of Stable Multiplicities in the Cohomology of Configuration Space

We describe an algorithm to compute the stable multiplicity of a family of irreducible representations in the cohomology of ordered configuration space of the plane. Using this algorithm, we compute the stable multiplicities of all families of irreducibles given by Young diagrams with \(23\) boxes o...

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Veröffentlicht in:arXiv.org 2024-11
1. Verfasser: Geisler, Emil
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Configurations
Homology
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description We describe an algorithm to compute the stable multiplicity of a family of irreducible representations in the cohomology of ordered configuration space of the plane. Using this algorithm, we compute the stable multiplicities of all families of irreducibles given by Young diagrams with \(23\) boxes or less up to cohomological degree \(50\). In particular, this determines the stable cohomology in cohomological degrees \(0 \leq i \leq 11\). We prove related qualitative results and formulate some conjectures.
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Homology
title Computations of Stable Multiplicities in the Cohomology of Configuration Space
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