Realization of U_q(so(N)) within the Differential Algebra on R_q^N

Abstract: We realize the Hopf algebra $U_{q^{-1}}(so(N))$ as an algebra of differential operators on the quantum Euclidean space $R_q^N$. The generators are suitable q-deformed analogs of the angular momentum components on ordinary $R^N$. The algebra $Fun(R_q^N)$ of functions on $R_q^N$ splits into a direct sum of irreducible vector representations of $U_{q^{-1}}(so(N))$; the latter are explicitly constructed as highest weight representations.