basically used the canonical intertwining operator $Y$ of type ${W\choose VW}$. It was known (\[FHL\], \[HL2\]) that there are canonical linear isomorphisms from the space of intertwining operators of type ${W\choose VW}$ to the space of intertwining operators of type ${V'\choose W'W}$. Let ${\cal{Y}}$ be an intertwining operator of type ${V'\choose W'W}$. (One can make use of the vacuum vector to get a canonical one.) Then ${\cal{Y}}(w',z)w$ is a linear functional on $V$. (To be rigorous we have to choose a branch of log function to evaluate $x$ at $z$ for ${\cal{Y}}(w',x)w$, see Section 4, or \[HL1\]. Here we neglect this issue for this introduction.) This gives another way to view $w'\otimes w$ as a linear functional on $V$. This time, for $u,v\in V$, the formal series $$\<Y(u,x){\cal{Y}}(w',z)w,v\>\;\;\;\;
\left(=\< {\cal{Y}}(w',z)w,Y^{o}(u,x)v\>\right)$$ by commutativity converges to a rational function in the domain $|x|>|z|$ with only two possible poles at $0$ and $z$, or a meromorphic function on $CP^{1}$ with only three possible poles at $0, z$ and $\infty$. Globally, evaluated intertwining operators ${\cal{Y}}(\cdot,z)\cdot$ at $x=z$ are exactly captured by the notion of $P(z)$-intertwining map (\[H3\], \[HL0-3\]). Then we consider linear functionals $\alpha$ on $V$ such that for $u,v\in V$, the formal series 