= Unitary highest-weight Virasoro module
{title2=$L_0|h\rangle=h|h\rangle,\quad L_n|h\rangle=0\ (n>0)$}
= Unitary highest-weight Virasoro representation
{synonym}
A <unitary highest-weight Virasoro module> is generated by a normalized vector satisfying the displayed relations, with a positive-definite <inner product> and $L_n^\dagger=L_{-n}$. Its <Virasoro descendants> have $L_0$ <eigenvalues> $h+N$ for nonnegative integral levels $N$. The <commutator> gives $\|L_{-1}|h\rangle\|^2=2h$, so <unitarity> requires $h\ge0$. Such a module is a quotient of a <Virasoro Verma module>; its <Unitary Virasoro discrete series> describes the cases with <central charge> below one.
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