摘要：In this talk, we first discuss the classifications of irreducible Whittaker modules for the generalized Heisenberg Lie algebra t and of irreducible Whittaker modules for the extended Lie algebra $\bar{t}$ obtained by adjoining degree derivations $d_1$, $d_2$, . . . , $d_m$ to t. Using these results, we construct imaginary Whittaker modules for non-twisted extended affine Lie algebras and prove that the imaginary Whittaker modules of $\mathbb{Z}$-independent level are always irreducible. This is a joint work with Yun Gao and Song Shi.