Generalized Verma module

Let ${\mathfrak {g}}$ be a semisimple Lie algebra and ${\mathfrak {p}}$ a parabolic subgalgebra of ${\mathfrak {p}}$. For any representation $V$ of ${\mathfrak {p}}$ we define the generalized Verma module to be

$M_{\mathfrak {p}}(V):={\mathcal {U}}({\mathfrak {g}})\otimes _{{\mathcal {U}}({\mathfrak {p}})}V$

See also:

Verma module