Frobenius characteristic map (source code)

= Frobenius characteristic map
{c}
{wiki}

The Frobenius characteristic map sends class functions on $S_n$ to homogeneous symmetric functions of degree $n$. It satisfies
$$
\operatorname{ch}(\chi^\lambda)=s_\lambda,
\qquad
\operatorname{ch}(\chi)=\sum_{\mu\vdash n}\frac{\chi(\mu)}{z_\mu}p_\mu.
$$