Constructing Homomorphisms between Verma Modules | Synapse
March 29, 2026Open Access
Constructing Homomorphisms between Verma Modules
Key Points
To develop a method for constructing nontrivial homomorphisms between Verma modules of semisimple Lie algebras.
Described a practical construction method for homomorphisms
Focused on nontrivial homomorphisms between two Verma modules
Extended the method to affine Lie algebra cases
Presented a systematic approach to obtain homomorphisms
Showed the applicability of the method to affine cases
Demonstrated that the method works for arbitrary semisimple Lie algebras
Abstract
We describe a practical method for constructing a nontrivial homomorphism between two Verma modules of an arbitrary semisimple Lie algebra.With some additions the method generalises to the affine case.