The polynomial question in modular invariant theory

Ami Braun (University of Haifa)

Wednesday 10th May, 2023 16:00-17:00 Maths 311B


Let G < GL(V) be a finite group ,where V is a finite dimensional vector space over a field F.
G acts as a group of automorphisms on S(V) ,the symmetric algebra on V.
We shall consider the following :

Q. When is S(V)^G ,the subring of G-invariants, a polynomial ring?

This had been completely settled by Shephard-Todd -Chevalley -Serre if  (charF, |G|)=1 ,and is still open otherwise.
We shall describe our solution to this problem when G< SL(V).
An application to the classification problem of isolated quotient singularities in prime characteristic, will be indicated.

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