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arXiv · 1211.1876

On the Top Degree of Coinvariants

Martin Kohls·Müfit Sezer
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Abstract

For a finite group $G$ acting faithfully on a finite dimensional $F$-vector space $V$, we show that in the modular case, the top degree of the vector coinvariants grows unboundedly: $\lim_{m\to\infty} \topdeg F[V^{m}]_{G}=\infty$. In contrast, in the non-modular case we identify a situation where the top degree of the vector coinvariants remains constant. Furthermore, we present a more elementary proof of Steinberg's theorem which says that the group order is a lower bound for the dimension of the coinvariants which is sharp if and only if the invariant ring is polynomial.

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Martin Kohls, Müfit Sezer. 2012-11-12. On the Top Degree of Coinvariants. https://doi.org/10.1093/imrn%2Frnt158

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