Generalized Verma module

Let ${\mathfrak {g}}$ be a semisimple Lie algebra and ${\mathfrak {p}}$ a parabolic subgalgebra of ${\mathfrak {g}}$ . 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:

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