A note on symmetric functions in Formanek polynomials
A note on symmetric functions in Formanek polynomials
Formanekâs proof of the existence of central identities has the following form: one constructs $n$ polynomials $G(X,{Y_1},{Y_2}, \cdots ,{Y_n}),G(X,{Y_2}, \cdots ,{Y_n},{Y_1})$, etc., whose sum is the desired central identity. The variables $X,{Y_i}$ are generic matrices. These $G$âs commute pairwise which raises the question whether all symmetric functions in them also …