Character generating series of symmetric powers
= Character generating series of symmetric powers
{title2=$\sum_{n\geq0}\chi_{S^nV}(g)t^n=\det(I-tg)^{-1}$}
For <eigenvalues> $\lambda_1,\ldots,\lambda_d$ of a finite-order linear action, its <symmetric power> characters satisfy $\sum_{n\geq0}\chi_{S^nV}t^n=\prod_j(1-\lambda_jt)^{-1}$. The denominator is the alternating generating <polynomial> of its <exterior power> characters.