Verma Module

Verma Module

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

The definition of a Verma module looks complicated, but Verma modules are very natural objects, with useful properties. Their homomorphisms correspond to invariant differential operators over flag manifolds.

Verma modules can be used to prove that an irreducible highest weight module with highest weight is finite dimensional, if and only if the weight is dominant and integral.