Symmetry offers a useful approach to unfold the intertwined degrees of freedom. Thus, it paves the way to resolving coexisting quantum orders into distinct symmetry sectors. Motivated by the recent observation of superconductivity (SC) in nanoflaked ${\mathrm{IrTe}}_2$, we investigate the SC in the strain-stabilized two-dimensional (2D) limit of ${\mathrm{IrTe}}_2$ by combining density functional theory with mean-field solution of the spin-fluctuation–mediated pairing interaction on a symmetry-constrained $\mathbf{k}·\mathbf{p}$ model. The spin-orbit–coupled band structure shows $\mathrm{\Gamma }$-centered Fermi sheets with existence of band-selective Rashba-like (in-plane) and Ising-like (out-of-plane) SC in the same compound. Remarkably, the SC gaps are odd in spin, orbital, and momentum channels despite the presence of global inversion symmetry. Fermi surface topologies and little-group symmetry enforce distinct irreducible representations to the Rashba and Ising channels, forbidding their mixing. Our findings open a symmetry-based route to multichannel SC in 2D transition-metal dichalcogenides with unique functionalities.

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• Electronic structure
• Spin fluctuations
• Superconductivity
• 2-dimensional systems
• Superconductors
• Density functional calculations
• Random phase approximation