B737-300
Air Traffic Control Fully Certified
Confusion; Situational Awareness
ATC Issue All Types; Conflict Airborne Conflict
Air Traffic Control Issued New Clearance
Human Factors
A B737 was level at FL330 and requesting FL350. When the B737 crossed into my boundary; I was able to climb him reference my own traffic. A couple minutes later; Sector 49 told me the B737 was good to climb to FL350 and I climbed the B737 to FL350. When I looked back to my screen; the B737 was flashing with an MD88 who was level at FL340. I turned the B737 20 degrees left and attempted to turn the MD88 20 degrees left but did not get a response; so I turned the B737 an additional 20 degrees left and told him to report when he was level at FL350. Then I turned the MD88 30 degrees left. I was a little busy at the time and had a test flight that I was trying to figure out what to altitude to climb to. When the ultra high controller says an aircraft is able to climb to a higher altitude; I should be more diligent in reviewing my own traffic before initiating the climb.
Enroute Controller described a loss of separation event when responding to an adjacent controllers comment reference a climb without first noting possible conflicting traffic within the area.