Verma module

Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics.

Verma modules can be used in the classification of irreducible representations of a complex semisimple Lie algebra. Specifically, although Verma modules themselves are infinite dimensional, quotients of them can be used to construct finite-dimensional representations with highest weight ${\displaystyle \lambda }$, where ${\displaystyle \lambda }$ is dominant and integral.^[1] Their homomorphisms correspond to invariant differential operators over flag manifolds.