M. Purificação Coelho, M. Antónia Duffner, Alexander E. Guterman
February 12, 2014
Let ∑ n (ℂ) denote the space of all n × n symmetric matrices over the complex field ℂ. The main objective of this paper is to prove that the maps Φ : ∑ n (ℂ) → ∑ n (ℂ) satisfying for any fixed irreducible characters χ, χ ': Sn → ℂ the condition d χ (A+αB) = d χ ' (Φ(A)+αΦ(B)) for all matrices A, B ∈ ∑ n (ℂ) and all scalars α ∈ ℂ are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ∑ n (ℂ).