Whittaker modules for Heisenberg algebras and imaginary Whittaker modules for affine Lie algebras
Whittaker modules for Heisenberg algebras and imaginary Whittaker modules for affine Lie algebras
复制标题
DOI：
10.1016/j.jalgebra.2008.06.025
复制
发表时间：
2008-10
影响因子：
0.9
通讯作者：
K. Christodoulopoulou
中科院分区：
文献类型：
--
作者：
K. Christodoulopoulou
我们分类了有限维和无限维Heisenberg代数的不可约Whittaker模，以及无限维Heisenberg代数的不可约Whittaker模。我们利用这些模构造了一类新的非扭曲仿射李代数模，我们称之为虚Whittaker模。证明了非零水平的虚Whittaker模是不可约的。
We classify the irreducible Whittaker modules for finite- and infinite-dimensional Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra. We use these modules to construct a new class of modules for non-twisted affine Lie algebras, which we call imaginary Whittaker modules. We show that the imaginary Whittaker modules of non-zero level are irreducible.