. Coefficientvector, Coeff = {}; l = {0}; sum = n*deg -(n*deg -ord)/2; VerifyList[l, deg, sum, n]; Return[Coeff] ) Now Coefficient[C4, CoefficientVector

. Sym, V (12) * ) (k)

C. ???, ?. ????, and C. ??-=, ) 8 , Q) 10 . This follows from MatrixRank, pp.1-16

. [. Bibliography, M. Alexeev, and . Brion, Moduli of Affine Schemes with Reductive Group Action, J. Algebraic Geometry, vol.14, pp.83-117, 2005.

P. Bravi, S. Cupit-foutoubk79, ]. W. Borho, and H. Kraft, Equivariant deformations of the affine multicone. Adv. in math ¨ Uber Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen, Comment. Math. Helv, vol.217, issue.1, pp.2800-2821, 1979.

N. Bourbaki, Groupes et algèbres de Lie, 1981.

M. Brion, On the representation theory of SL(2), Indagationes Mathematicae, vol.5, issue.1, pp.29-36, 1994.
DOI : 10.1016/0019-3577(94)90030-2

A. Clebsch, Theorie der binären algebraischen Formen, 1872.

S. Cupit-foutou, Invariant Hilbert schemes and wonderful varieties. arXiv:math

J. Dixmier, Polarisation dans les algèbres de Lie semi-simples complexes, Bull. Sci. Math, vol.99, pp.45-63, 1975.

W. Fulton and J. Harris, Representation Theory: A First Course, 2000.

R. Hartshorne, Algebraic Geometry, 1977.
DOI : 10.1007/978-1-4757-3849-0

M. Haiman and B. Sturmfels, Multigraded Hilbert schemes, Journal of Algebraic Geometry, vol.13, issue.4, pp.725-769, 2004.
DOI : 10.1090/S1056-3911-04-00373-X

J. Humphreysja05-]-s and . Jansou, Linear Algebraic Groups Déformations des cônes de vecteurs primitifs. arXiv:math, p.506133, 1975.

S. Jansou and N. Ressayre, Invariant deformations of orbit closures in sl n . Represent, pp.50-62, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00157519

J. C. Jantzen, Representations of algebraic groups, 1987.
DOI : 10.1090/surv/107

H. Kraft and C. Procesi, Classical Invariant Theory ? A Primer, 1996.

H. Kraft, Geometrische Methoden in der Invariantentheorie. Friedr, 1985.

H. Kraft and J. Weyman, Degree Bounds for Invariants and Covariants of Binary Forms, 1999.

A. Cohen, M. Van-leeuwen, B. Lisser, and . Lie, A Computer algebra package, available at http://www-math.univ-poitiers.fr/~maavl/LiE/index, Matsushima. Espaces homogènes de Stein des groupes de Lie complexes, pp.81-105, 1960.

H. Matsumura, Commutative Ring Theory, 1986.
DOI : 10.1017/CBO9781139171762

D. Mumford, J. Fogarty, and F. Kirwan, Geometric Invariant Theory, 1994.