[AAIIIC]

CTS-V was factory supercharged.

No, it wasn't - the first generation were N/A LS6s and LS2s.

I have a 2006 CTS V with the LS-2 that was supercharged by a previous owner. The belt tensioner that is on it needs to be replaced but Nobody can come up with tge same thing I have. When adding a supercharger to a first gen CTS V LS-2, is there a specific belt tensioner that is commonly used? View attachment 597451

That's a Magnuson supercharger kit. They have a bunch of tensioners listed on their website, so you can start there. I would guess that they use an OEM part repurposed for their kit, so it may be possible to find the tensioner cheaper; I'll update your thread title to be more specific in the hopes that your fellow "Maggie" owners will see this thread and chime in.