Can 3 dimensional Heisenberg group be represented irreducibly on L^2(S)?

Question

It is well-known that unitary dual of the 3 dimensional Heisenberg group H represented on $L^2(\mathbb{R})$ is given by a nonzero real number $\lambda\in R^*$(can be interpreted as $1/\hbar$). When $\lambda=1/\hbar=0$, the unirreps are all 1 dimensional. My question is if H can also be represented irreducibly on $L^2(\mathbb{S})$ with $\mathbb{S}$ denoting the 1 dimensional compact manifold---circle.