M. Bucero, C. Bajaj, and B. Mourrain, On the construction of general cubature formula by flat extensions, Structured Matrices: Theory and Applications, vol.502, pp.104-125, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01158099

M. Bucero and B. Mourrain, Border basis relaxation for polynomial optimization, Journal of Symbolic Computation, vol.74, pp.378-399, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00981546

A. Arnold, Sparse Polynomial Interpolation and Testing, vol.3, 2016.

A. Arnold, M. Giesbrecht, and D. Roche, Sparse interpolation over finite fields via low-order roots of unity, ISSAC 2014-Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, pp.27-34, 2014.

A. Arnold and E. Kaltofen, Error-correcting sparse interpolation in the Chebyshev basis, Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '15, pp.21-28, 2015.

A. Arnold and D. Roche, Multivariate sparse interpolation using randomized Kronecker substitutions, ISSAC 2014-Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, pp.35-42, 2014.

T. Becker and V. Weispfenning, Gröbner Bases -A Computational Approach to Commutative Algebra, 1993.

M. Ben-or and P. Tiwari, A deterministic algorithm for sparse multivariate polynomial interpolation, Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC '88, pp.301-309, 1988.

A. Bernardi, D. Taufer, and . Waring, tangential and cactus decompositions, 2018.

J. Berthomieu, B. Boyer, and J. Faugère, Linear algebra for computing Gröbner bases of linear recursive multidimensional sequences, Journal of Symbolic Computation, vol.83, pp.36-67, 2017.

N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines. Actualités Scientifiques et Industrielles, No. 1337, 1968.

N. Bourbaki, Éléments de mathématique. Fasc. XXXVIII: Groupes et algèbres de Lie. Chapitre VII: Sous-algèbres de Cartan,éléments réguliers. Chapitre VIII: Algèbres de Lie semi-simples déployées. Actualités Scientifiques et Industrielles, No. 1364, 1975.

J. Brachat, P. Comon, B. Mourrain, and E. Tsigaridas, Symmetric tensor decomposition, Linear Algebra Appl, vol.433, pp.1851-1872, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00355713

M. Collowald and E. Hubert, A moment matrix approach to computing symmetric cubatures, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01188290

M. Collowald and E. Hubert, Algorithms for computing cubatures based on moment theory, Studies in Applied Mathematics, vol.141, issue.4, pp.501-546, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01873077

D. Cox, J. Little, and D. O'shea, An introduction to computational algebraic geometry and commutative algebra, Undergraduate Texts in Mathematics, 2015.

D. A. Cox, J. Little, and D. O'shea, Using algebraic geometry, Graduate Texts in Mathematics, vol.185, 2005.

J. Dieudonné-;-providence and R. I. , Special functions and linear representations of Lie groups, CBMS Regional Conference Series in Mathematics, vol.42, 1979.

A. Dress and J. Grabmeier, The interpolation problem for k-sparse polynomials and character sums, Adv. in Appl. Math, vol.12, issue.1, pp.57-75, 1991.

W. Fulton and J. Harris, Representation theory, Graduate Texts in Mathematics, vol.129, 1991.

K. Gatermann and P. A. Parrilo, Symmetry groups, semidefinite programs, and sums of squares, J. Pure Appl. Algebra, vol.192, issue.1-3, pp.95-128, 2004.

M. Giesbrecht, G. Labahn, and W. Lee, Symbolic-numeric sparse polynomial interpolation in Chebyshev basis and trigonometric interpolation, CASC 2004, 2004.

M. Giesbrecht, G. Labahn, and W. Lee, Symbolic-numeric sparse interpolation of multivariate polynomials, J. Symbolic Comput, vol.44, issue.8, pp.943-959, 2009.

W. H. Greub, Die Grundlehren der Mathematischen Wissenschaften, vol.97, 1967.

D. Grigoriev, M. Karpinski, and M. Singer, The interpolation problem for k-sparse sums of eigenfunctions of operators, Adv. in Appl. Math, vol.12, issue.1, pp.76-81, 1991.

B. Hall, Lie groups, Lie algebras, and representations, vol.222

M. Hoffman and W. Withers, Generalized Chebyshev polynomials associated with affine Weyl groups, Trans. Amer. Math. Soc, vol.308, issue.1, pp.91-104, 1988.

Q. Huang, An improved early termination sparse interpolation algorithm for multivariate polynomials, J. Syst. Sci. Complex, vol.31, issue.2, pp.539-551, 2018.

J. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, vol.9, 1972.

E. Imamogli and E. Kaltofen, On computing the degree of a Chebyshev polynomial from its value, 2018.

E. Kaltofen and Y. Lakshman, Improved sparse multivariate polynomial interpolation algorithms, Symbolic and algebraic computation, vol.358, pp.467-474, 1988.

E. Kaltofen and W. Lee, Early termination in sparse interpolation algorithms, International Symposium on Symbolic and Algebraic Computation (ISSAC'2002, vol.36, pp.365-400, 2003.

E. Kaltofen, W. Lee, and A. Lobo, Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm, Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation, pp.192-201, 2000.

S. Kunis, T. Peter, T. Römer, and U. Von-der-ohe, A multivariate generalization of Prony's method, Linear Algebra Appl, vol.490, pp.31-47, 2016.

Y. Lakshman and D. Saunders, Sparse polynomial interpolation in nonstandard bases, SIAM J. Comput, vol.24, issue.2, pp.387-397, 1995.

J. B. Lasserre, Moments, positive polynomials and their applications, vol.1, 2010.

M. Laurent, Sums of squares, moment matrices and optimization over polynomials, Emerging applications of algebraic geometry, vol.149, pp.157-270, 2009.

H. Li and Y. Xu, Discrete Fourier analysis on fundamental domain and simplex of A d lattice in dvariables, J. Fourier Anal. Appl, vol.16, issue.3, pp.383-433, 2010.

M. Lorenz, Invariant Theory and Algebraic Transformation Groups, Encyclopaedia of Mathematical Sciences, vol.135, 2005.

C. Lubich, From quantum to classical molecular dynamics: reduced models and numerical analysis, Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), 2008.

V. D. Lyakhovsky and P. V. Uvarov, Multivariate Chebyshev polynomials, J. Phys. A, vol.46, issue.12, p.22, 2013.

R. Moody, L. Motlochová, and J. Patera, Gaussian cubature arising from hybrid characters of simple Lie groups, J. Fourier Anal. Appl, vol.20, issue.6, pp.1257-1290, 2014.

R. Moody and J. Patera, Computation of character decompositions of class functions on compact semisimple Lie groups, Math. Comp, vol.48, issue.178, pp.799-827, 1987.

R. Moody and J. Patera, Cubature formulae for orthogonal polynomials in terms of elements of finite order of compact simple Lie groups, Adv. in Appl. Math, vol.47, issue.3, pp.509-535, 2011.

B. Mourrain, Polynomial-exponential decomposition from moments, Foundations of Computational Mathematics, vol.18, issue.6, pp.1435-1492, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01367730

H. Munthe-kaas, M. Nome, and B. Ryland, Through the kaleidoscope: symmetries, groups and Chebyshev-approximations from a computational point of view, Foundations of computational mathematics, vol.403, pp.188-229, 2011.

M. Nesterenko, J. Patera, and A. Tereszkiewicz, Orthogonal polynomials of compact simple Lie groups, Int. J. Math. Math. Sci, 2011.

V. Pereyra and G. Shcerer, Exponential Data Fitting and its Applications. Bentham e-books, 2010.

D. Potts and M. Tasche, Sparse polynomial interpolation in Chebyshev bases, Linear Algebra Appl, vol.441, pp.61-87, 2014.

S. Power, Finite rank multivariable Hankel forms, Linear Algebra Appl, vol.48, pp.237-244, 1982.

C. , Baron de Prony) Riche. Essai expérimental et analytique sur les lois de la dilatabilité des fluide? elastique et sur celles de la force expansive de la vapeur de l'eau et de la vapeur de l'alkool,à différentes températures, J. de l'École Polytechnique, vol.1, pp.24-76, 1795.

C. Riener, T. Theobald, L. J. Andrén, and J. B. Lasserre, Exploiting symmetries in SDP-relaxations for polynomial optimization, Math. Oper. Res, vol.38, issue.1, pp.122-141, 2013.

B. Ryland and H. Munthe-kaas, On multivariate Chebyshev polynomials and spectral approximations on triangles, Spectral and high order methods for partial differential equations, vol.76, pp.19-41, 2011.

S. Sakata, ;. Sala, S. Sakata, T. Mora, C. Traverso et al., The BMS algorithm, Gröbner Bases, Coding, and Cryptography, pp.143-163, 2009.

T. Sauer, Prony's method in several variables: symbolic solutions by universal interpolation, J. Symbolic Comput, vol.84, pp.95-112, 2018.

J. Serre, Algèbres de Lie semi-simples complexes, 1966.

N. Vilenkin, Special functions and the theory of group representations. Translated from the Russian by V, N. Singh. Translations of Mathematical Monographs, vol.22, 1968.