On a conjecture of Hivert and Thiery about Steenrod operators

We prove some results related to a conjecture of Hivert and Thiéry about the dimension of the space of q-harmonics. In the process we compute the actions of the involved operators on symmetric and alternating functions, which have some independent interest. We then use these computations to prove other results related to the same conjecture.We prove some results related to a conjecture of Hivert and Thiéry about the dimension of the space of q-harmonics (F. Hivert and N. Thiéry, 2004 [HT]). In the process we compute the actions of the involved operators on symmetric and alternating functions, which have some independent interest. We then use these computations to prove other results related to the same conjecture. © 2012 Elsevier Inc