Extending the coinvariant theorems of Chevalley, Shephard-Todd, Mitchell, and Springer

Abraham Broer; Victor Reiner; Larry Smith; Peter Webb

doi:10.1112/plms/pdq027

Extending the coinvariant theorems of Chevalley, Shephard-Todd, Mitchell, and Springer

Abraham Broer, Victor Reiner, Larry Smith, Peter Webb

Mathematics

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9 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	747-785
Number of pages	39
Journal	Proceedings of the London Mathematical Society
Volume	103
Issue number	5
DOIs	https://doi.org/10.1112/plms/pdq027
State	Published - Nov 2011

Bibliographical note

Funding 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.

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AU - Webb, Peter

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AB - 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.

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Extending the coinvariant theorems of Chevalley, Shephard-Todd, Mitchell, and Springer

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