We prove that the monoid of generic extensions of finite-dimensional nilpotent k[T]-modules is isomorphic to the monoid of partitions (with addition of partitions). This gives us a simple method for computing generic extensions, by addition of partitions. Moreover we give a combinatorial algorithm that calculates the constant terms of classical Hall polynomials.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-11,
author = {Justyna Kosakowska},
title = {Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {253-261},
zbl = {1285.16008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-11}
}
Justyna Kosakowska. Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials. Colloquium Mathematicae, Tome 126 (2012) pp. 253-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-11/