Computing component groups of stabilizers of nilpotent orbit representatives

We describe computational methods for computing the component group of the stabilizer of a nilpotent element in a complex simple Lie algebra. Our algorithms have been implemented in the language of the computer algebra system GAP4. Occasionally we need Gröbner basis computations; for these we use th...

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Bibliographic Details
Published in:Journal of symbolic computation 2025-07, Vol.129, p.102404, Article 102404
Main Authors: Di Bella, Emanuele, de Graaf, Willem A.
Format: Article
Language:English
Subjects:
Component group
Computational methods
Nilpotent orbits
Semisimple Lie algebra
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Summary:We describe computational methods for computing the component group of the stabilizer of a nilpotent element in a complex simple Lie algebra. Our algorithms have been implemented in the language of the computer algebra system GAP4. Occasionally we need Gröbner basis computations; for these we use the systems Magma and Singular. The resulting component groups have been made available in the GAP4 package SLA.
ISSN:0747-7171
DOI:10.1016/j.jsc.2024.102404