On a conjecture of Hivert and Thiéry about Steenrod operators (Q448404)

\textit{F. Hivert} and \textit{N. M. Thiéry} [in: Campbell, H. E. A. Eddy (ed.) et al., Invariant theory in all characteristics. Proceedings of the workshop on invariant theory, Queen's University, Kingston, ON, Canada, April 8--19, 2002. Providence, RI: American Mathematical Society (AMS). CRM Proceedings \& Lecture Notes 35, 91--125 (2004; Zbl 1125.55010)] considered the differential operator \(\sum_{i=1}^n(\partial_i^k+qx_i\partial_i^{k+1})\), where \(k \geq 1\) and \(q\) denotes a formal parameter, which generates the \(q\)-Steenrod algebra over \(\mathbb{C}[q]\) (\(q=1\) gives the rational Steenrod algebra introduced by Wood and \(q=0\) gives the algebra generated by generalized Laplacians).NEWLINENEWLINENEWLINENEWLINEIn this paper the authors prove some results related to a conjecture of Hivert and Thiéry about the dimension of the space of \(q\)-harmonics (polynomials of \(\mathbb{C}[q][x_1,\dots, x_n]\) annihilated by the above family of differential operators).