I have a problem at my work - I feel like my analyst has switched their behaviour and is becoming hostile to me. We are currently managing our own projects where I don’t lead them, but any attempt at checking their work (it’s still my responsibility) is met with pushback/elusiveness. I raised a point to my boss saying that I feel they are hostile to what he said I should be less controlling and more collaborative. I tried to invite to talk over lunch/coffee but they said they are busy with work

Oh gosh. I'm so sorry you're faced with this at work. I hate that walking on eggshells feeling. And I'm bummed that your boss wasn't more helpful, but either way, you're on the right track with wanting to work this out. I try to put myself in the other's shoes and wonder what caused that behavior switch. Maybe something is going on outside of work that's trickling in, or can you think of any instances at work that would cause them to put that wall up? Coffee might feel awkward to them, or the timing might just be off. Is their work generally good? I'd give them some room to breathe while checking on their work from afar (if possible).

I'm sorry that's a difficult situation. I would keep trying to reach out to them and if it's been a month of no action then it's worth another talk with your boss and this time come with documentation.

Yikes. That sounds like a tough situation to be in. If they aren't willing to sit down and chat with you, then there may not be much you can do. I would probably stop asking about their work and let them do their thing. If they mess up then you can tell your boss that you tried to be collaborative and they weren't embracing it so you let them take the lead.

Update, I talked with them and apparently they don’t like when I arrive without a context to ask what they are working on while they have pre-validated it with my n+1. I.e. I arrive asking what’s up on the project while it was clear for them that they are working on it. I said that I am arriving more as to help, to get into the thing and understand what’s happening because I will need to back them up and it’s easier to be 2 on the project

And I said hey we will collaborate on the future projects so tell me what’s up, so I know, otherwise it would be complicated if I don’t know right?

Extremely tricky but I would try giving them some space and looking to rebuild the relationship.