Invariant polynomials on tensors under the action of a product of orthogonal groups (Q2796525)
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scientific article; zbMATH DE number 6560462
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariant polynomials on tensors under the action of a product of orthogonal groups |
scientific article; zbMATH DE number 6560462 |
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Invariant polynomials on tensors under the action of a product of orthogonal groups (English)
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29 March 2016
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invariant polynomial
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orthogonal group
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dimension
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matching
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permutation
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tensor product
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This paper studies the tensor product \(V\) of defining representations for a finite direct product \(K\) of orthogonal groups. The main result is a stable formula for the dimension of the K-invariant algebra of degree \(d\) homogeneous polynomial functions on \(V\). The main ingredient in the proof is a formula for a number of fixed point free involutions which commute with a given permutation. Additionally, a bijection between a basis for the space of invariants and the isomorphism classes of certain graphs is described.
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