ZOB Controller experienced loss of separation event when he/she assumed adjacent airspace was combined and descended traffic; resulting in a confliction. Corrective action was too late.

Narrative

End of shift; Supervisor was combining sectors into the midnight configuration. I had just assumed the adjacent super high sector. I was now working sectors 38 and 39. These sectors have a base altitude of FL330. After a while the Supervisor came around and told me; 'you have it all.' I took that to mean I was also assuming the intermediate highs ( FL 240-FL320). I looked down to the Controller who was at that sector and saw that he/she was turned away from the scope and talking to a trainee. I believed I then indeed had that airspace. A minute later I descended Air Carrier X from my base to FL 290 to meet the LOA for Boston Center. Immediately upon descent the conflict alert went off with an aircraft at FL320. I then saw the Controller react and then realized he/she was indeed still open. I heard him/her turn her aircraft left. I turned my aircraft 60 degrees north. Loss of separation occurred with 3 miles and 300 feet. Recommendation; its hard to say since the error occurred due to my perceived 'sectorization.' This is a routine that is followed every night and a lack of specific awareness as to who was still open led to my error. From the Supervisor's standpoint; to announce from behind me that I 'had it all' was vague and led me to assume that which was not true. However; that does not release me from the fact I still had clues that the sector was open below me; i.e. I had not assumed the frequencies. This is simply an awareness issue that demonstrates complacency and attention to detail can lead to this type of error.