摘要
Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.
Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.
基金
N. Jing＇s work was partially supported by the Simons Foundation （Grant No. 198129） and the National Natural Science Foundation of China （Grant No. 11271138）, and he also acknowledged the hospitality of Max-Planck Institute for Mathematics in the Sciences at Leipzig during this work.
