I was once hired for a core team job. Between my hire and the first day, the core team manager resigned and I was reassigned, so I did not have much chance to work with him.
Instead, I landed in a middle of a drama. The previous core team manager was a servant leader, delivering bare minimum and helping on administrative and organizational matters. He was the loosing party, preparing to quit and passing affairs. By virtue of being hired by this guy, I was considered his protégé by the new core team manager.
That new manager was operating by decrees, and his first decrees were naturally targeted at everyone who could have undermined his authority, including me. Instead of helping he was setting standards and mandating bills of materials. Older product teams mostly ignored him, but new ones were suffering. By the time I left, the guy had a promotion.
Lesson learnt? Core teams win by imposing, not helping.