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

Abstract

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).