The Capelli identity, the double commutant theorem, and multiplicity-free actions (Q810147)
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scientific article; zbMATH DE number 4212313
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Capelli identity, the double commutant theorem, and multiplicity-free actions |
scientific article; zbMATH DE number 4212313 |
Statements
The Capelli identity, the double commutant theorem, and multiplicity-free actions (English)
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1991
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The Capelli identity of Classical Invariant Theory is discussed in the context of multiplicity-free actions of algebraic groups on vector spaces. All possible generalizations of the Capelli Identities in this setting are discussed, using a classification of irreducible multiplicity-free actions by Kac. It is explained how these identities permit one to compute b-functions studied earlier by Shimura and Rubenthaler-Schiffmann. Several results on ideal theory and orbits for multiplicity-free actions are also given.
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invariant differential operator
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enveloping algebra
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Capelli identity
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Invariant Theory
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multiplicity-free actions
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algebraic groups
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b- functions
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orbits
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0.86966836
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0.8665184
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0.86304843
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0.8616681
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