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Highest-weight representation

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For a Borel subalgebra $\mathfrak b=\mathfrak t\oplus\mathfrak n^+$ and a weight $\lambda$, the Verma module is
$$
M_\lambda=U(\mathfrak g)\otimes_{U(\mathfrak b)}\mathbb C_\lambda,
$$
where $\mathfrak n^+$ kills $\mathbb C_\lambda$ and $h\in\mathfrak t$ acts by $\lambda(h)$.


Verma module

Paper 102 / 2 / i / Solution

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A Verma module is a type of representation of a highest weight module in the context of the representation theory of Lie algebras, particularly those that are semisimple. Verma modules play an important role in the study of the structure and representation theory of Lie algebras and quantum groups.


Verma module ( $M_{λ}$ )

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Verma module (Mλ​)

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