I am looking for literature on entrywise invariant kernels. The specific example I have in mind is $K:R^{d}\times R^{d}\to R$ and locally compact groups acting on vector space $R^{d}$. More precisely I am looking to find properties of the eigenvectors and eigenvalues of kernels such that for any elements of the group $g,h\in R^{d\times d}$ I have $K(gx,hy)=K(x,y)$. Any suggestion? Thanks! Fabio