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Degenerations of Submodules and Composition Series

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Let M and N be modules over an artin algebra such that M degenerates to N. We show that any submodule of M degenerates to a submodule of N. This suggests that a composition series of M will in some sense degenerate to a composition series of N. We then study a subvariety of the module variety, consisting of those representations where all matrices are upper triangular. We show that these representations can be seen as representations of composition series, and that the orbit closures describe the above mentioned degeneration of composition series.

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Correspondence to Nils M. Nornes.

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Presented by Steffen Koenig.

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Nornes, N.M., Oppermann, S. Degenerations of Submodules and Composition Series. Algebr Represent Theor 20, 803–819 (2017). https://doi.org/10.1007/s10468-017-9677-0

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  • DOI: https://doi.org/10.1007/s10468-017-9677-0

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