On the natural representation of $S(\Omega )$ into $L^2(P(\Omega ))$: Discrete harmonics and Fourier transform

José Manuel Marco, Javier Parcet

Let $\Omega$ denote a non-empty finite set. Let $S(\Omega )$ stand for the symmetric group on $\Omega$ and let us write $P(\Omega )$ for the power set of $\Omega$. Let $\rho :S(\Omega )\to U(L^2(P(\Omega )))$ be the left…