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Combinantal Forms of a Quadric Net Applied to Irreducible Concomitant Systems

Published online by Cambridge University Press:  20 January 2009

T. Scott
T. Scott
Affiliation:
Department of Mathematics, Heriot-Watt College, Edinburgh
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A complete system of combinantal forms (generalised and ordinary) of a pencil of quadrics fλ ≡ λ1f1 + λ2f2 can be chosen such that the coefficients of the various power products of λ1, λ2 in the former give a complete irreducible system of concomitants of the two quadrics f1, f2, and conversely. This result was proved by Todd (1), who used it in conjunction with Schur function analysis (2) (3) to derive the complete irreducible system of concomitants of two quaternary quadratics (4).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 12 , Issue 4 , December 1961 , pp. 189 - 195
Copyright
Copyright © Edinburgh Mathematical Society 1961

References

REFERENCES

(1) Todd, J. A., Combinants of a pencil of quadric surfaces, Proc. Camb. Phil. Soc, 43 (1947), 478–480.Google Scholar
(2) Littlewood, D. E., Invariant theory, tensors and group characters, Phil. Trans. Roy. Soc. (A), 239 (1944), 305–369.Google Scholar
(3) Todd, J. A., On syzygies connected with the covariant line complexes of two quadric surfaces, Proc. L.M.S., 51 (1950), 325–347.Google Scholar
(4) Todd, J. A., The complete irreducible system of two quaternary quadrics, Proc. L.M.S., 52 (1951), 1–13.Google Scholar
(5) Turnbull, H. W., The invariant theory of three quadrics, Proc. L.M.S., 20 (1922), 465–489.CrossRefGoogle Scholar
(6) Williamson, J., The linear complexes belonging to the invariant system of three quadrics, Proc. Edin. Math. Soc, 42 (1924), 29–40.CrossRefGoogle Scholar
(7) Turnbull, H. W., The Theory of Determinants, Matrices and Invariants (Blackie, 1945).Google Scholar
(8) Capelli, A., Sopra le Forme Algebriche Ternarie à piu Serie di Variabili, Giorn. di Mat., 18 (1880), 17–33.Google Scholar
(9) Elliott, E. B., An Introduction to the Algebra of Quantics (Oxford, 1895).Google Scholar