A B777 ON A VECTOR AT FL330 WAS ERRONEOUSLY CLRED TO FL370 BY A ZID ARTCC RADAR CTLR RESULTING IN A LOSS OF SEPARATION WITH A C560 LEVEL AT FL350 ON AN ASSIGNED DIRECT ROUTING.

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B777 CLBING TO FL370 E; AND C560 DSNDING N. CONFLICT ALERT ACTIVATED. I SHIPPED ACFT TO OTHER CTLR FOR CTL INSTRUCTIONS IMMEDIATELY. SUPPLEMENTAL INFO FROM ACN 639100: C560 AT FL350 WAS SWITCHED TO NEXT SECTOR. B777 INTERIM AT FL330. D-SIDE TO D-SIDE COORD CLB TO FL370. NEITHER ACFT WERE ON FREQ. B777 SHOULD HAVE JUST BEEN LEFT AT FL330. IT WAS BUSY AND A LOT OF ACFT WERE TRANSITIONING ALT. SUPPLEMENTAL INFO FROM ACN 639099: I WAS WORKING WAB SH RADAR. C560 CHKED ON MY FREQ LEVEL AT FL350. B777 WAS A POINTOUT TO MY SECTOR AT FL330; EVENTUALLY CLBING TO FL370. I OBSERVED B777'S CODE C AT FL334 AND IN A CLB CONFIGN. FL330 WAS STILL IN THE DATA BLOCK AS A TEMPORARY ALT. THE ACFT WERE NOW IN A CONFLICTION STATUS AND NEITHER ACFT WERE IN THE LATERAL CONFINES OF MY AIRSPACE. I CALLED THE BATESVILLE SH RADAR CTLR AND INFORMED THEM THAT I WAS TURING C560 HARD L. I THEN ISSUED A CLRNC TO C560 TO TURN L TO A HDG OF 270 DEGS. THE ACFT RESPONDED; 'TURNING TO A 270 DEG HDG; WE HAVE THE TFC IN SIGHT!' AS OF THIS TIME; I UNDERSTAND THAT THERE WAS A COMS BREAKDOWN BTWN 2 SECTORS AND THEIR SECTOR TEAMS; JUST S OF MY SECTOR. SUPPLEMENTAL INFO FROM ACN 639708: WE WERE NBOUND AT FL350; GOING DIRECT TO PVT VOR (APPROX 350 DEG HDG). CTLR ISSUED AN IMMEDIATE TURN TO 270 DEGS; WITH SUBSEQUENT INSTRUCTION FOR AN EXPEDITED DSCNT TO FL330. AS WE STARTED THE TURN; WE RECEIVED A TA (TCASII ONLY INSTALLED) AND NOTED AN AIRLINER AT OUR 12 O'CLOCK POS; EBOUND; AT FL350. IT BECAME OBVIOUS THAT THE HDG CHANGE; AND SUBSEQUENT ALT CHANGE; WOULD ELIMINATE THE COLLISION THREAT. IN SPEAKING TO A SUPVR AT THE CTR; IT IS MY UNDERSTANDING THAT THE CTLR HAD MADE AN ERROR IN NOTING THE CORRECT ALT ON THE AIRLINER'S DATA BLOCK. THERE WAS ALSO AN ERROR WITH THE AIRLINER BEING ON THE INCORRECT FREQ.