Is it unusual for them to send an invitation a few days before the interview. The other two universities gave me at least a week notice.
I was away and HR didn't read my out-of-office reply, but I got an email on Weds night (which should have been Thursday morning except I checked when I got home) inviting me for an interview on Friday for my current job. They were able to put me off till Monday (only because they had another candidate coming that day), but no further.