  The generalized quantum Euclidean group $\oq(\frak{b}_{m,n})$ is a natural
generalization of the quantum Euclidean group $\oq(\frak{b}_{1,1})$. The
Heisenberg double $\od(\frak{b}_{m,n})$ of $\oq(\frak{b}_{m,n})$ is the smash
product of $\oq(\frak{b}_{m,n})$ with its Hopf dual $\ou(\frak{b}_{m,n})$. In
this paper, we study the weight modules, the prime spectrum and the
automorphism group of the Heisenberg double $\od(\frak{b}_{m,n})$.
