Robert Carter, the man in charge of running the Republican National Convention, sat back in his third-floor office amid the elephant paraphernalia and doled out some favors to his friends from Washington.

At his side was Bob Pyle, a colleague on the newly elected D.C. Republican Committee, who had brought Carter a list of 23 home town political buddies who needed tickets to the convention.

"Loyalty," said cnvention manager Carter, smiling as he reached into desk drawer and pulled out the necessary tickets. "We've got to take care of the Rebuild people."

The "Rebuild people" are members of the District's Committee to Rebuild the Republican Party, a recently formed conservative, and predominantly white, faction that won 63 of the 70 seats on the D.C. Republican Committee last May. It was during that power coup that Carter, Pyle and other Ward 3 Reagan supporters took control of the city's small Republican Party.

None of the faction's members won delegate seats at the convention -- the 14 District of Columbia delegates are all Bush supporters from the ousted progressive wing of the local party. Still, as Carter's act of ticket patronage indicated, it is the Rebulid fraction that has the power and control in Detroit.

Not only do they have impressive jobs -- such as Carter's -- on the convention staff, they also have the prized hotel rooms close to Cobo Hall. The official delegation is stuck a half hour away in a Detroit suburb.

Carter, the new D.C. Republican chairman, said today that he plans to offer an olive branch to the defeated progressives. "Some people will be sore losers," he said. "But I intend to get this party back together again and start building up the organization."

In an exaggerated symbol of his willingness to mend the wounds, Carter reached into another desk drawer and said: "I'll show you how nice we are. I've got tickets her for all the D.C. delegates to go to the reception."

"There's not a Reagan supporter in the delegation, but they're all going to get tickets," added Henry Berliner, another Rebuild member working here with the Regan committee.

Of the 23 Rebuild committee members already in Detroit, Carter is convention manager, Robert Gleason is in charge of planning the convention's transportation, Stan Anderson is the convention's general counsel, Michael Gill is in charge of program planning, Clarance V. McKee heads Regan's personal task force on minorities and Fred Dixon is the tally clerk who will add up the votes on nomination night.

They are the District of Columbia's shadow delegation in Detroit, meeting as a group every morning for coffee and rolls. Berliner was even quoted in one Detroit daily newspaper, and identified mistakenly as a "District of Columbia delegate."

The members of the official delegation, Republican moderates comitted to George Bush, have become increasingly isolated at a convention dominated by the party's right wing. The District of Columbia delegation was forced to sidetrack its own plans to push for a D.C. voting rights plank in the party's platform, after being scared off by the platform committee's overwhelmingly conservative majority.

The Rebuild committee members, meanwhile, are in the Republican party's mainstream at this convention. They endorsed Reagan for president after the Illinois primary when, in the words of Rebuild member, "we felt it was al over."

The same Rebuild member said privately that back in Washington the Reagan supporters stand to gain many patronage jobs and coveted access to the White House, should Regan win the presidency

Carter said that there still is some animosity between the two sides in the local Republican Party, "But it's the type of thing that goes away."

As the new chairman of the local party, Carter said, he can appoint 25 additional members to the ruling Republican committee. He said he will appoint the 25 District of Columbia precinct chairmen who do the best job turning out the vote for Ronald Regan and for local Republican City Council candidates in the Nov. 4 election. If some of the defeated party leaders stay active, they can get their committee positions back again.

"There are those who will want to stay active," Carter said. "Then there are those who are committed to some philosophy or ideology. We don't have any room for them."

Carter said there had been " a festering of discontent about the party's lack of organization and lack of communication. Now is the time to start building up the party from the precinct level."

He looked across the desk to Bob Pyle, who reminded him about a Monday morning breakfast meeting for the D.C. Republicans.

"Don't forget to invite some of the delegates," Carter said, smiling.