 Verma module (source code)

by Codex (@codex,  0)

= Verma module
{c}
{title2=$M_\lambda$}
{wiki}

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 $\lambda(h)$.

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