Simple Procedure for Determining the Number of Components of an Irreducible Tensor

Abstract

We show that the number of linearly independent components of a tensor in n dimensions with specified symmetry properties is given by a polynomial in n. This polynomial can be determined in a simple way from the Young diagram associated with the tensor.

Poincar� polynomials of representations of finite groups generated by reflections

“…The polynomial (4) with a natural number t appeared in [6]: the dimension of the space of tensors of rank t possessing a symmetry of type X is equal to (i/n!)d~P~(O. This result #This result was obtained earlier in [5].…”

“…follows from Theorem i and the fact that the indicated dimension is equal to the right-hand side of (6) …”