On the Mathieu conjecture for \(S U(2)\) (Q475592)

The Mathieu conjecture [\textit{O. Mathieu}, in: Algèbre non-commutative, groupes quantiques et invariants. Septième contact Franco-Belge, Reims, France, June 26--30, 1995. Paris: Société Mathématique de France. 263--279 (1995; Zbl 0889.22008)] is related to the Jacobian conjecture, since it implies the Jacobian conjecture, see [\textit{S. Smale}, Math. Intell. 20, No. 2, 7--15 (1998; Zbl 0947.01011)] and [\textit{A. van den Essen}, Polynomial automorphisms and the Jacobian conjecture. Basel: Birkhäuser (2000; Zbl 0962.14037)]. The Mathieu conjecture was proved for abelian compact groups in [\textit{J. J. Duistermaat} and \textit{W. van der Kallen}, Indag. Math., New Ser. 9, No. 2, 221--231 (1998; Zbl 0916.22007)]. The paper under review is devoted to study the Mathieu conjecture for \(S U(2)\) using the matrix elements of its unitary irreducible representations.