Groups of linear operators defined by group characters
Marvin D. Marcus, James Holmes · Transactions of the American Mathematical Society · 1972
Some of the recent work on invariance questions can be regarded as follows: Characterize those linear operators on $\operatorname {Hom} (V,V)$ which preserve the character of a given representation of the full linear group. In this paper, for certain rational characters, necessary and sufficient conditions are described that ensure that the set of all such operators forms a group $\mathfrak {L}$. The structure of $\mathfrak {L}$ is also determined. The proofs depend on recent results concerning derivations on symmetry classes of tensors.