The drafting subcommittee of the Democratic Platform Committee began work on a party platform yesterday with forces loyal to President Carter clearly in command.

Outwardly, rival representatives of Carter and Sen. Edward M. Kennedy (Mass.) expressed satisfaction that the subcommittee was working harmoniously, but beneath these formal assurances each side sniped at the other.

The Carter camp said that is was offering olive branches, but that the Kennedy group was breaking them and hurling them to the ground. The Kennedy camp said there were no olive branches.

Kennedy supporters gave the press copies of a draft platform prepared by the Democratic National Committee's staff that called for a tax cut in 1981. This caused a flutter of interest until it was learned that Stuart Eizensat, the president's senior adviser on domestic affairs, specifically disavowed the pledge for the tax cuts next year and asked that the section be redrafted.

Kennedy loyalists on the drafting subcommittee (they total five of the 15) formally proposed that a draft platform submitted by the senator be made the working draft for the subcommittee. This idea was rejected, 9 to 3 (two Kennedy members were absent.)

The Kennedy draft asked for all the things Kennedy has been proposing during his campaign this year, and also made several new suggestions. One would commit the party to take no new fiscal or budgetary action that would cause additional unemployment. Another would favor immediate reimposition of oil price controls -- 180 degrees from Carter's decontrol policy.

The drafting subcommittee made no final decisions. It will continue deliberations today.