What is IR active, Raman active?

Example 5.22 (Carbon dioxide and the greenhouse)

$\ce{CO2}$ has a centre of inversion. Its symmetric stretch ($\Sigma_g^+$, $1333\,\mathrm{cm}^{-1}$) is Raman active only; the antisymmetric stretch ($\Sigma_u^+$, $2349\,\mathrm{cm}^{-1}$) and the bend ($\Pi_u$, $667\,\mathrm{cm}^{-1}$) are IR active only. The bend absorbs near $15\,\text{µ}\mathrm{m}$, close to the peak of the Earth’s thermal emission: the reason carbon dioxide is a greenhouse gas. $\ce{N2}$ and $\ce{O2}$ have a single, $\Sigma_g^+$, vibration: IR inactive.

Example 5.25 (Cis and trans)

cis-$\ce{ML4(CO)2}$, $C_{2v}$: characters $2, 0, 2, 0$, $\Gamma_{\mathrm{CO}} = A_1 + B_1$, two IR bands. trans-$\ce{ML4(CO)2}$, $D_{4h}$: $\Gamma_{\mathrm{CO}} = A_{1g} + A_{2u}$, one IR band ($A_{2u}$) and one Raman band ($A_{1g}$). A single CO band in the infrared means trans.