Can I share my 1 bedroom apartment with a roommate?

I live in New York, in a 1 bedroom rent stabilized building. My name is currently on the lease. Is it legally possible to share my apartment with a roommate? I’ll occupy the living room while the roommate will occupy the bedroom. My lease states that I need to inform the landlord if a new occupant moves in. Do I legally have to inform my landlord and obtain a special permission if the occupant stays for more than 30 days? What If she stays for 29 days or less? Am I allowed to have an occupant stay for such a short time and how much am I allowed to charge my roommate for rent? (a little over half ok?)