P _c resonances in the compact pentaquark picture

$P_c$ resonances are studied in the approach of quark model and group theory. It is found that there totally 17 possible pentaquark states with contents $q^3Q \bar Q$ ($q$ $u$ $d$ quarks; $Q$ $c$ quark) compact picture, where hidden heavy may take color singlet-singlet ($[111]_{{qqq}}\otimes [111]_{{c c}}$) octet-octet ($[21]_{{qqq}}\otimes [21]_{{c configurations. The partial decay widths calculated for all channels. results show $pJ/\psi$ dominant channel both spin $3/2$ $1/2$ states, indicate $P_c(4440)$ not be a state while $P_c(4312)$ $P_c(4457)$ could spin-$\frac{1}{2}$ spin-$\frac{3}{2}$ respectively.