The polynomial question in modular invariant theory, old and new

Amiram Braun (University of Haifa)

Wednesday 16th May, 2018 16:00-17:00 Maths 110


Let G be a finite group, V a finite-dimensional G-module over a field F, and S(V) the symmetric algebra of V. The above problem seeks to determine when the corresponding invariant ring S(V)^G is a polynomial ring. In the non-modular case (where the characteristic of F is prime to the order of G), this was settled in the Shephard-Todd theorem. The modular case (where the characteristic of F divides the order of G) is still wide open. I shall discuss some older results due to Serre, Nakajima, Kemper-Malle, and explain some new results, mostly in dimension 3.

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