When the hardline supporters of the Shah gather these days, they meet in a palatial house at the end of Zahedi Avenue, named for the general who rallied the army to the shah's support when he returned to power in 1953.

Now the house belongs to the general's son, Ardeshir Zahedi, Iran's ambassador to Washington, whom opponents of the shah suspect of desiring to repeat his father's achievement.

The gregarious diplomat whose lavish parties and generosity with caviar have made him a Washington favorite has been playing a very different role here in Tehran.

Power broker, negotiator, confidant to the shah, unofficial spokesman for the regime, Zahedi has been one of the most conspicuous actors in the current Iranian drama.

He is the purported leader of a group popularly known as the "Hesarak faction," which for weeks has been at the center of Tehran's limitless political gossip.It was credited with and blamed for fomenting military coups, promoting or sabotaging a political solution to the crisis, urging the shah to do this or that or warning him against it.

One Western diplomat said flatly that the group supported the new government of Prime Minister Shahpour Bakhtiar as the only available formula that might salvage the shah's throne. Another diplomat in the same embassy said with equal certainty that the Hesarak faction opposed Bakhtiar.

The Hesarak faction, if it exists at all, is not a formal organization. It is a term used to describe a group of diplomats, politicians and military officers generally described as "hardliners." These are diehard supporters of the shah who have done what they can to keep him on the throne with as much of his remaining power as he can salvage.

The group draws its name from an exclusive neighborhood in the hills overlooking Tehran where the members have met at Zahedi's home.

Now a new civilian government has been installed and Zahedi is returning to Washington. Even that news has inspired conflicting theories about its significance.

One is that Zahedi is leaving because the hardliners have lost out with the installation of the new government. Another view is that he is leaving because he succeeded in putting together the best available deal under the circumstances, preserving the monarchy.

A third view was expressed by Ahmad Tehrani, former ambassador to South Africa and a junior member of the Hesarak faction.

"He's the ambassador in Washington, after all," Tehrani said. "He's in here six weeks for consultations and it's only natural that he should resume his duties."

The truth is probably a combination of all three. In any case, with Zahedi's departure following that of Gen. Gholamali Oveissi, the martial law commander who was ousted last week, the Hesarak faction will not be what it was.

Zahedi, who enjoys talking to the press, has been readily available for background discussions about the political maneuvering, but he would not submit to an interview about his own role in it.

A western diplomat said Zahedi envisioned himself as "his father's son, who thinks he can do the same thing."

Zahedi, 50, has made no secret of his loyalty to the shah and his belief that the shah should not only keep his throne but also continue to wield power in the country.

He was formerly married to Princess Shanaz, the shah's daughter by his first marriage, and is said to have business connections with the Pahlavi family. As late as October, he was reported to be seeking the post of court minister, but the shah is said to have told him to return to the United States to keep an eye on Crown Prince Reza, who is undergoing training with the U.S. Air Force in Texas.

Zahedi believes the Iranian army could still restore order by getting tougher with strikers and demonstrators, but says the shah has been ordering restraint to minimize bloodshed. His opposition critics, and some diplomats, believe that he counseled the shah to turn the army loose. "A very firm hand is going to be needed," one source quoted him as saying.

Opposition leaders have denounced Zahedi as a kind of Persian Rasputin, manipulating the monarch for his own ends. They claim that the shah would have left the country by now if Zahedi had not talked him out of it.

Western diplomats say that while Zahedi is naturally working hard to save a regime to which his personal fortunes are tied, it was a group of military officers who approached the shah and asked him to stay, although Zahedi may well have encouraged them.

In Washington, Zahedi is renowned for promoting the image of Iran through lavish parties. Martial law and an early evening curfew have limited social life here. But Zahedi managed to convene the American press corps for cocktails and political reassurance on New Year's Eve.

The night before, a bulletin saying the shah was abdicating had been flashed around the world. Zahedi pooh-poohed the tale, saying that his "worst mistake" had been to arrange a return to Iran of the correspondent who sent the story. The correspondent had been expelled for an earlier journalistic act that the government considered a transgression.

At the party Zahedi introduced the press to Gen. Oanuchehr Hotrowdad, a hardline officer who assured the press of the military's devotion to the shah.

Zahedi, educated at the University of Utah and a one-time foreign minister, has been ambassador to the United States since 1973 and an important link in the shah's chain of political and military ties to the United States.

With that relationship changed and Prime Minister Bakhtiar calling for a new Iranian foreign policy, diplomats here believe that Zahedi may be nearing the end of his tenure in Washington.