On the Poincaré series of representations of finite reflection groups (Q1316828)
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scientific article; zbMATH DE number 525655
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Poincaré series of representations of finite reflection groups |
scientific article; zbMATH DE number 525655 |
Statements
On the Poincaré series of representations of finite reflection groups (English)
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12 April 1994
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Shorter proofs of some known results [\textit{A. A. Kirillov} and \textit{I. M. Pak}, Funkts. Anal. Prilozh. 24, No. 3, 9-13 (1990)] are given on the Poincaré series for the symmetric group \(S_ n\) acting in \(\mathbb{R}^ n\) by permutation of coordinates and for the octahedral group \(Q_ n\) acting in \(\mathbb{R}^ n\) by permutation of coordinates and alternation of signs. Also certain corollaries are produced, a conjecture is stated and for other infinite series of finite reflection groups the formulas are written.
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symmetric group
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octahedral group
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finite reflection groups
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