Generic extensions of nilpotent $k[T]$-modules, monoids of partitions and constant terms of Hall polynomials

Volume 128 / 2012

Justyna Kosakowska 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.

Authors

  • Justyna KosakowskaFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail

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