Quantum Knizhnik-Zamolodchikov equation associated with $U_q(A_2^{(2)})$ for $\mathrm{\mid }q\mathrm{\mid }=1$

We present an integral representation to the quantum Knizhnik-Zamolodchikov equation associated with twisted affine symmetry $U_q(A_2^{(2)})$ for massless regime $\mathrm{\mid }q\mathrm{\mid }=1$. Upon specialization, it leads to a conjectural formula for the correlation function of the Izergin-Korepin model in massless regime $\mathrm{\mid }q\mathrm{\mid }=1$. In a limiting case $q\to -1$, our conjectural formula reproduce the correlation function for the Izergin-Korepin model at xritical point $q=-1$.