Do GP pay incentive feed to LP or the other way around?

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LP to GP.

Commonly, the GP is the manager of the fund, so he is who mostly make the investment decisions.

I agree with you too, but CFAI glossary says GP pays to LP, which confuses me.

I would follow what the reading says, that specific glossary word is wrong. Found in the reading text of the CFAI book and Schweser, even on Investopedia and Wikipedia, that is LP to GP, not otherwise.

Regards