Abstract
In the note, for an action which is the tensor product of the tautological action of the unimodular group of three-dimensional space and the second symmetric power of the tautological action of the unimodular group of three-dimensional space, the orbits are classified and the generators of the algebra of invariants are described.
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REFERENCES
É. B. Vinberg, “The Weyl group of a graded Lie algebra,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 40 (1976), no. 3, 488-526.
É. B. Vinberg and A. G. Élashvili, “A classification of the three-vectors of nine-dimensional space,” in: Trudy Sem. Vektor. Tenzor. Anal. [in Russian], vol. 18, Moskov. Gos. Univ., Moscow, 1978, pp. 197-233
G. C. Shephard and J. A. Todd, “Finite unitary reflection groups,” Canad. J. Math., 6 (1954), no. 2, 274-304.
A. G. Nurmiev, “Orbits and invariants of third-order matrices,” Mat. Sb. [Math. USSR-Sb.], 191 (2000), no. 5, 101-108.
T. A. Springer, Invariant Theory, Lecture Notes Math., vol. 585, Springer-Verlag, Berlin-New York, 1977.
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Artamkin, D.I., Nurmiev, A.G. Orbits and Invariants of Third-Order Cubic Matrices with Symmetric Fibers. Mathematical Notes 72, 447–453 (2002). https://doi.org/10.1023/A:1020572026013
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DOI: https://doi.org/10.1023/A:1020572026013