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arXiv · 1406.6299

Degree of reductivity of a modular representation

Martin Kohls·Müfit Sezer
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Abstract

For a finite dimensional representation $V$ of a group $G$ over a field $F$, the degree of reductivity $\delta(G,V)$ is the smallest degree $d$ such that every nonzero fixed point $v\in V^{G}\setminus\{0\}$ can be separated from zero by a homogeneous invariant of degree at most $d$. We compute $\delta(G,V)$ explicitly for several classes of modular groups and representations. We also demonstrate that the maximal size of a cyclic subgroup is a sharp lower bound for this number in the case of modular abelian $p$-groups.

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Martin Kohls, Müfit Sezer. 2014-06-24. Degree of reductivity of a modular representation. https://doi.org/10.1142/s0219199716500231

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