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arXiv · 2102.07290

On Numbers of Tuples of Nilpotent Matrices over Finite Fields under Simultaneous Conjugation

Jiuzhao Hua
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Abstract

The problem of classifying tuples of nilpotent matrices over a field under simultaneous conjugation is considered "hopeless". However, for any given matrix order over a finite field, the number of concerned orbits is always finite. This paper gives a closed formula for the number of absolutely indecomposable orbits using the same methodology as Hua [5]; those orbits are non-splittable over field extensions. As a consequence, those numbers are always polynomials in the cardinality of the base field with integral coefficients. It is conjectured that those coefficients are always non-negative.

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BibTeXRIS

Jiuzhao Hua. 2021-02-15. On Numbers of Tuples of Nilpotent Matrices over Finite Fields under Simultaneous Conjugation. https://arxiv.org/abs/2102.07290

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