On a problem of Pommerening in invariant theory (Q1825961)
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scientific article; zbMATH DE number 4122228
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a problem of Pommerening in invariant theory |
scientific article; zbMATH DE number 4122228 |
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On a problem of Pommerening in invariant theory (English)
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1989
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\textit{K. Pommerening} showed [in Math. Z. 176, 359-374 (1981; Zbl 0438.14010)], that if \(G=SL_ n\) and H is a subgroup of G which is obtained from the unipotent radical of a parabolic subgroup by removing any set of simple roots then the algebra of regular functions on G which are H-invariant with respect to the action of H on G by right translations is finitely generated. In the paper under review Pommerening's theorem is partially generalized to arbitrary semisimple groups G (though for \(G=SL_ n\) the results are weaker than Pommerening's).
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finite generation
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algebra of invariants
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unipotent radical
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parabolic subgroup
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simple roots
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algebra of regular functions
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action
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semisimple groups
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