Symmetry adapted Gram spectrahedra. (English) Zbl 1472.90083
Summary: This paper explores the geometric structure of the spectrahedral cone, called the symmetry adapted positive semidefinite (PSD) cone, and the symmetry adapted Gram spectrahedron of a symmetric polynomial. In particular, we determine the dimension of the symmetry adapted PSD cone, describe its extremal rays, and discuss the structure of its matrix representations. We also consider the symmetry adapted Gram spectrahedra for specific families of symmetric polynomials including binary symmetric polynomials, quadratics, and ternary quartics and sextics which give us further insight into these symmetric sums of squares polynomials.
MSC:
| 90C22 | Semidefinite programming |
| 05E05 | Symmetric functions and generalizations |
| 14Q30 | Computational real algebraic geometry |
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