Rational invariants of even degree polynomials under the orthogonal group
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909525195358208 |
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| author | Breloer, Henri |
| author_facet | Breloer, Henri |
| contents | In this article, we construct a generating set of rational invariants for the action of the orthogonal group $\text{O}(n)$ on the space $\mathbb{R}[x_1,\dots,x_n]_{2d}$ of real homogeneous polynomials of even degree $2d$. This generalizes a paper which addressed the case $n=3$. The main difficult with the generalization lies in a surprising connection to the graph isomorphism problem, a classical problem of computer science. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational invariants of even degree polynomials under the orthogonal group Breloer, Henri Commutative Algebra 13A50 (Primary), 05C60, 68W30 (Secondary) In this article, we construct a generating set of rational invariants for the action of the orthogonal group $\text{O}(n)$ on the space $\mathbb{R}[x_1,\dots,x_n]_{2d}$ of real homogeneous polynomials of even degree $2d$. This generalizes a paper which addressed the case $n=3$. The main difficult with the generalization lies in a surprising connection to the graph isomorphism problem, a classical problem of computer science. |
| title | Rational invariants of even degree polynomials under the orthogonal group |
| topic | Commutative Algebra 13A50 (Primary), 05C60, 68W30 (Secondary) |
| url | https://arxiv.org/abs/2501.17504 |