Any introvert managers with tips on how to handle things?

I'm a computer programmer by trade, which normally seems to be a pretty good fit for an introvert. However, it seems that in the very near future my job description is going to shift from mostly programming with a bit of technical decision making in meetings to something more like full on project management - handling the day to day tasking of ~20 people, including handing out assignments, keeping track of progress, scheduling, running meetings, and settling disputes.

Are any of you introverts working as managers? I'm kind of nervous about stepping into the role, especially the settling disputes part (which is something that will happen, given how opinionated and stubborn programmers can often get). Any advice on how to deal with it?