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 to prove that an irreducible highest weight module with highest weight ${\displaystyle \lambda }$ is finite-dimensional, if and only if the weight ${\displaystyle \lambda }$ is dominant and integral. Their homomorphisms correspond to invariant differential operators over flag manifolds.

The definition relies on a stack of relatively dense notation. Let ${\displaystyle F}$ be a field and denote the following:

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