# Reduction formula for infinite group order?

In group theory, what do we do when we have infinite group order, like in D∞h or C∞v but we want to mathematically determine the SALCs (symmetry adapted linear combinations) using the projection formula. If we did, we would get a function that tends towards 0 which isn't that useful. I asked my lecturer, and he suggested that it's probably because it's obvious with linear molecules so we wouldn't need to mathematically determine the SALCs. Is there some way of doing it though?

• This is an interesting question, but I think it'd benefit from having a specific, concrete example. I also think it'd help if you explicitly wrote out this function which "tends towards 0" and how you obtained it. Oct 30, 2022 at 20:53
• Generally when working SALCs for $D_{\infty h}$ or $C_{\infty v}$, you use a subgroup like $D_{2h}$ or $C_{2v}$ using an equivalence table or "descent in symmetry" table between the irreducible representations. For example the Jacobs University tables for $D_{\infty h}$ indicate the A / E representations as well as $\Sigma$, $\Pi$, $\Delta$ etc. Oct 31, 2022 at 0:06
• Since 9 months have gone by with no answers, I think it's fair to let you know about Matter Modeling Stack Exchange which also answers group theory questions, but make sure to delete the question from here if you're cross-posting there (or to at least put a note at the top of your question, saying that it's cross-posted). Aug 8 at 2:29