# Connection between irreducible representations and electronic states in diatomic molecules

I am trying to understand the connection between irreducible representations and molecular electronic states. To explain the problem: I found some potential energy curves (PECs) for $$\ce{N2+}$$ in the form of irreducible representations such as $$\mathrm{A_g}$$, $$\mathrm{A_u}$$, $$\mathrm{B_{2g}}$$, ...

However, in the literature, I normally find the PECs in the form of $$\Sigma$$, $$\Pi$$, $$\Delta$$... states. How do we connect these two pictures? I am not an expert in quantum chemistry calculations. A simple explanation will be highly helpful.

In the linear $$C_{\infty \mathrm{v}}$$ and $$D_{\infty \mathrm{h}}$$ point groups there are two notations for the irreducible representations which are equivalent, in that
\begin{align} \mathrm{A_1} &\equiv \Sigma^+ \\ \mathrm{A_2} &\equiv \Sigma^- \\ \mathrm{E_1} &\equiv \Pi \\ \mathrm{E_2} &\equiv \Delta \\ \mathrm{E_3} &\equiv \Phi \\ &\,\,\vdots \end{align}
For $$C_{\infty \mathrm{v}}$$, these are the actual irreps; for $$D_{\infty \mathrm{h}}$$ you simply need to tack on a g or u label to denote the symmetry with respect to inversion. See e.g. the $$D_{\infty \mathrm{h}}$$ character table found at http://symmetry.jacobs-university.de/cgi-bin/group.cgi?group=1001&option=4 which contains both notations.