On Noether's and Weyl's bound in positive characteristic

Details On Noether's and Weyl's bound in positive characteristic On Noether's and Weyl's bound in positive characteristic

2002-07-22

arxiv.org/abs/math/0207194v2

Invariant theory in all characteristics, 175-188, CRM Proc. Lecture Notes, 35, Amer. Math. Soc., Providence, RI, 2004

Mathematics

Representation Theory

16 pages, v2: minor changes, final version

Scientific paper

In this note we generalize several well known results concerning invariants of finite groups from characteristic zero to positive characteristic not dividing the group order. The first is Schmid's relative version of Noether's theorem. That theorem compares the degrees of generators of a group with those of a subgroup. Then we prove a suitable positive characteristic version of Weyl's theorem on vector invariants: polarization works in small degrees. Using that we show that the regular representation has the "most general" ring of invariants, thereby generalizing theorems of Schmid and Smith.

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