Unitary Virasoro discrete series (source code)

= Unitary Virasoro discrete series
{c}
{title2=$c=1-6/[m(m+1)],\quad h_{r,s}=([(m+1)r-ms]^2-1)/[4m(m+1)]$}

An irreducible unitary <highest weight> module of the <Virasoro algebra> with $c<1$ has integer $m\ge2$, $1\le r\le m-1$, $1\le s\le m$, and the displayed weights. Labels $(r,s)$ and $(m-r,m+1-s)$ represent the same module. It is obtained from the <Verma module> by quotienting its zero-norm submodules; the two generating singular-vector levels are $rs$ and $(m-r)(m+1-s)$. For $m=2$ this is the trivial $c=h=0$ module. For $m=3$, the three weights are $0$, $1/2$, $1/16$.