Generators of invariant rings and modular representations of symmetric groups (Q2861002)
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scientific article; zbMATH DE number 6225604
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generators of invariant rings and modular representations of symmetric groups |
scientific article; zbMATH DE number 6225604 |
Statements
11 November 2013
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invariant theory
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unstable algebra
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pseudoreflection group
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Lie group
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classifying space
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Generators of invariant rings and modular representations of symmetric groups (English)
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Let \(W(G)^*\) be the dual representation of the Weyl group, \(W(G)\), of a compact connected Lie group, \(G\). In [Trans. Am. Math. Soc. 350, No. 12, 4919--4930 (1998; Zbl 0901.55009)], \textit{W. G. Dwyer} and \textit{C. W. Wilkerson} prove that the invariant ring, \(H^*(BT^{p-1};\mathbb{F}_{p})^{W(SU(p))^*}\), is not a polynomial algebra if \(p\geq 5\). In the paper under review, the authors obtain another proof of this result for \(p=5\) and \(p=6\) from the determination of some generators of the invariant ring.
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