Classification on irreducible Whittaker modules over quantum group U_q（{\mathfrak{s}\mathfrak{l}}_{\mathrm{3}},\wedge ）

Abstract

We define the Whittaker modules over the simply-connected quantum group U_q（{\mathfrak{s}\mathfrak{l}}_{\mathrm{3}},\wedge ） ; where \wedge is the weight lattice of Lie algebra {\mathfrak{s}\mathfrak{l}}_{\mathrm{3}}: Then we completely classify all those simple ones. Explicitly, a simple Whittaker module over U_q（{\mathfrak{s}\mathfrak{l}}_{\mathrm{3}},\wedge ） is either a highest weight module, or determined by two parametersz\in ℂ\text{} and\gamma \in {ℂ}^{*}\text{} (up to a Hopf automorphism).

Key words： Quantum group; simple; Whittaker module; Whittaker vector

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