  We report an angle-resolved photoemission spectroscopy (ARPES) study on a
triangular lattice superconductor Ir$_{1-x}$Pt$_{x}$Te$_2$ in which the Ir-Ir
or Te-Te bond formation, the band Jahn-Teller effect, and the spin-orbit
interaction are cooperating and competing with one another. The Fermi surfaces
of the substituted system are qualitatively similar to the band structure
calculations for the undistorted IrTe$_2$ with an upward chemical potential
shift due to electron doping. A combination of the ARPES and the band structure
calculations indicates that the Te $5p$ spin-orbit interaction removes the
$p_x/p_y$ orbital degeneracy and induces $p_x \pm ip_y$ type spin-orbit
coupling near the A point. The inner and outer Fermi surfaces are entangled by
the Te $5p$ and Ir $5d$ spin-orbit interactions which may provide exotic
superconductivity with singlet-triplet mixing.
