Classification on irreducible Whittaker modules over quantum group U_q( 𝔰𝔩_3, Λ)

We define the Whittaker modules over the simply-connected quantum group U_q( 𝔰𝔩_3, Λ) , where Λ is the weight lattice of Lie algebra 𝔰𝔩_3 . Then we completely classify all those simple ones. Explicitly, a simple Whittaker module over U_q( 𝔰𝔩_3, Λ) is either a highest weight module, or determined by two parameters z ∈ ℂ and γ ∈ ℂ* (up to a Hopf automorphism).