We extend in several directions invariant theory results of Chevalley, Shephard-Todd, Mitchell, and Springer. Their results compare the group algebra for a finite reflection group with its coinvariant algebra, and compare a group representation with its module of relative coinvariants. Our extensions apply to arbitrary finite groups in any characteristic.
Bibliographical noteFunding Information:
The work of the first-named author was supported by NSERC. The work of the second-named author was supported by NSF grant DMS-0245379. The work of the fourth-named author was supported by MSRI.