On the irreducibility of Professor G. F. Smith's representations for isotropic functions (Q1819967)

Irreducibility is proved of the basis for scalar-valued isotropic functions due to \textit{G. F. Smith} [ibid. 9, 899-916 (1971; Zbl 0233.15021)], once the redundant elements found by \textit{J. P. Boehler} are eliminated [Z. Angew. Math. Mech. 57, 323-327 (1977; Zbl 0362.15019)]. Similarly Smith's basis for vector-valued, second order skew-symmetric tensor-valued and second order symmetric tensor-valued isotropic functions are proved irreducible. An argument by \textit{J. J. Telega} [Arch. Math. 36, 147-162 (1984; Zbl 0571.73040)] leading to reducibility of the last of them is proved incorrect.