SDP Feasibility Problems and sos Representation Ranks for OT-FKM Type Isoparametric Polynomials
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917356661374976 |
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| author | Ge, Jianquan Jia, Kai Zhao, Yuyang |
| author_facet | Ge, Jianquan Jia, Kai Zhao, Yuyang |
| contents | Semidefinite programming (SDP) provides a fundamental framework for studying properties of sum-of-squares (sos) representations of nonnegative polynomials. In this paper we study the quartic forms GF = (|x|^4 + F(x))/2 associated with isoparametric polynomials F of OT-FKM type with g = 4. We characterize the sos property of GF in terms of the feasibility of an explicit SDP determined by the underlying Clifford system, and in the sos cases we obtain quantitative rank bounds for sos representations, with rigidity when m >= 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21241 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SDP Feasibility Problems and sos Representation Ranks for OT-FKM Type Isoparametric Polynomials Ge, Jianquan Jia, Kai Zhao, Yuyang Differential Geometry Algebraic Geometry Optimization and Control 53C40, 14P99, 90C22, 15A63 Semidefinite programming (SDP) provides a fundamental framework for studying properties of sum-of-squares (sos) representations of nonnegative polynomials. In this paper we study the quartic forms GF = (|x|^4 + F(x))/2 associated with isoparametric polynomials F of OT-FKM type with g = 4. We characterize the sos property of GF in terms of the feasibility of an explicit SDP determined by the underlying Clifford system, and in the sos cases we obtain quantitative rank bounds for sos representations, with rigidity when m >= 3. |
| title | SDP Feasibility Problems and sos Representation Ranks for OT-FKM Type Isoparametric Polynomials |
| topic | Differential Geometry Algebraic Geometry Optimization and Control 53C40, 14P99, 90C22, 15A63 |
| url | https://arxiv.org/abs/2603.21241 |