Automorphisms of the ring of invariants of the binary quintic representation of SL2
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911803512979456 |
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| author | Daigle, Daniel Freudenburg, Gene |
| author_facet | Daigle, Daniel Freudenburg, Gene |
| contents | Let k^[6] denote a polynomial ring in 6 variables over an algebraically closed field k of characteristic zero and consider the action of SL2(k) on k^[6] induced by the irreducible representation of SL2 of degree 5 (the binary quintic representation). We consider the ring Q = (k^[6])^SL2 of invariant polynomials and show that Aut_k(Q) = u(k), the unit group of k, where Aut_k(Q) is the group of k-algebra automorphisms of Q. Based on this result, we show that the group of SL2-equivariant polynomial automorphisms of k^[6] is isomorphic to u(k). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphisms of the ring of invariants of the binary quintic representation of SL2 Daigle, Daniel Freudenburg, Gene Commutative Algebra Algebraic Geometry 14R20, 14L35, 13N15, 13A50 Let k^[6] denote a polynomial ring in 6 variables over an algebraically closed field k of characteristic zero and consider the action of SL2(k) on k^[6] induced by the irreducible representation of SL2 of degree 5 (the binary quintic representation). We consider the ring Q = (k^[6])^SL2 of invariant polynomials and show that Aut_k(Q) = u(k), the unit group of k, where Aut_k(Q) is the group of k-algebra automorphisms of Q. Based on this result, we show that the group of SL2-equivariant polynomial automorphisms of k^[6] is isomorphic to u(k). |
| title | Automorphisms of the ring of invariants of the binary quintic representation of SL2 |
| topic | Commutative Algebra Algebraic Geometry 14R20, 14L35, 13N15, 13A50 |
| url | https://arxiv.org/abs/2403.12681 |