= Virasoro Verma module
{c}
{title2=$M(c,h)$}
= Verma module of the Virasoro algebra
{c}
{synonym}
= Verma modules of the Virasoro algebra
{c}
{synonym}
The <Virasoro Verma module> $M(c,h)$ is the universal <highest-weight representation> with <central charge> $c$ and ground weight $h$. The <Poincaré-Birkhoff-Witt theorem> gives a basis $L_{-n_1}\cdots L_{-n_s}|h\rangle$ with $n_1\ge\cdots\ge n_s>0$. Its invariant Hermitian form is fixed by $L_n^\dagger=L_{-n}$ and the norm of the ground vector. Quotienting by its maximal proper submodule produces the irreducible highest-weight module; in the unitary cases this removes the null vectors.
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