On independent sets of basis functions for irreducible representations of finite groups

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Abstract
Two theorems on bases of irreducible representations of finite groups are compared. It is stressed that their validity depends upon the functional sets for which they are formulated. The first theorem, which states that there are as many linearly independent (modulo the identity representation) sets of basis functions as is the dimension of the representation, is shown to hold only if the considered functional set constitutes a field. Otherwise, more such sets are necessary as shows the second theorem (extended Noether’s theorem), which is limited to polynomial algebra. The second theorem seems to be more apt for explicit construction of functional bases.