Generic extensions of nilpotent $k[T]$-modules, monoids of partitions and constant terms of Hall polynomials
Volume 128 / 2012
Colloquium Mathematicum 128 (2012), 253-261
MSC: Primary 16D10; Secondary 16G10, 16G20, 05A17.
DOI: 10.4064/cm128-2-11
Abstract
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.
