Poincaré series on symmetric and alternating tensors for irreducible representations of imprimitive complex reflection groups (Q1337440)

The unitary reflection groups are classified by Shephard and Todd. There are two infinite families, \(G_{n,r}\) and \(G_{n,r,p}\), of irreducible reflection groups, and besides them, only a finite number of irreducible ones exist. We consider the irreducible decomposition of the tensor product of the symmetric tensors and the alternating tensors of the natural representation of \(G_{n,r}\) and \(G_{n,r,p}\).