Classification on irreducible Whittaker modules over quantum group $${U_q}\left( {{\mathfrak{s}\mathfrak{l}_3},\,{\rm{\Lambda }}} \right)$$

We define the Whittaker modules over the simply-connected quantum group $${U_q}\left( {{\mathfrak{s}\mathfrak{l}_3},\,{\rm{\Lambda }}} \right)$$ , where Λ is the weight lattice of Lie algebra $${\mathfrak{s}\mathfrak{l}_3}$$ . Then we completely classify all those simple ones. Explicitly, a simple Whittaker module over $${U_q}\left( {{\mathfrak{s}\mathfrak{l}_3},\,{\rm{\Lambda }}} \right)$$ is either a highest weight module, or determined by two parameters z ∈ ℂ and γ ∈ ℂ* (up to a Hopf automorphism).