A lavender ceramic star shines on Elizabeth Taylor's dressing room door at the Kennedy Center Opera House. Beside her star, another shoots across the door--a green satin soft sculpture star with tinsel rays and above it the word "Alvin."

Taylor, with Alvin the Parrot perched delicately on her arm, but without Victor Gonzalez Luna the Fiance' (who reportedly has returned to Mexico), left the Vista Hotel yesterday for her first performance in "Private Lives" at the Kennedy Center.

Taylor, resplendent in her favorite purple, a blouse over pants, made a grand entrance into the Vista's solarium lobby. A group of about 35 people, many of them TWA flight attendants, stood and applauded. Alvin had no comment.

Taylor smiled, tucked her arm through the arm of her personal security guard, and shook her head at the thought of autographs. The word went out that she was having just a small quiver of first-night jitters, even though the official opening isn't until Sunday night. Alvin looked a shade flighty.

Her Kennedy Center dressing room has been redone in her honor, in her favorite shades of pale lavender for the walls and a pearl gray carpet. A copy of a Monet waterlily pool, mostly greens and purples, hangs on the wall.

In the dressing rooms of Taylor and her costar, ex-husband Richard Burton, are separate-but-equal silver-framed photographs of Taylor, Burton and playwright Noel Coward at the Ascot Races. Taylor's producer, Zev Bufman, gave them to the stars as an opening night gift.

Before the show, Taylor had supper with Bufman at the Intrigue restaurant in the Watergate complex. Then Taylor and Bufman walked up from the restaurant to the Kennedy Center stage door. They were trailed by her limousine.

"Michael Longeran, company mangager, got her started walking, along the river in Philadelphia," said Bufman.

Burton, who's staying at the Watergate Hotel, took the luxurious route, arriving in his limousine.

The stars' arrival was observed by only one fan, Richard Ecker, a Falls Church teacher, who said he really came to see John Cullum, the second male lead in "Private Lives" and a free-lance photographer.

Another star currently playing the Kennedy Center, Al Pacino, in "American Buffalo" at the Terrace Theater, slipped into the center earlier in the afternoon unobserved.

Meanwhile, back at the Vista, quite an entourage is engaged in watching after Elizabeth Taylor. One whole room of the Givenchy-decorated Presidential Suite has been cleared of its double beds to hold Taylor's clothes. Satellite rooms house her personal secretary, body guard and hairdresser. Her manager, Chen Sam, and Bufman have Givenchy-decorated suites as well, on other floors.

Alvin shares Taylor's private bedroom. He has a commodious cage (The rug below it is protected by a sheet of 4-by-4-foot plywood), as well as two other perches elsewhere in the suite. Alvin, somewhat of a nighthawk, dislikes going back into the cage. Today, Alvin received a letter, marked "Personal and Confidential." A rumor says the letter came from a love bird (a parrot-amour?).

The Presidential Suite initially was stocked with Taylor's favorite, Taittinger Comtes de Champagne Rose' 1975. The hotel has laid in several more bottles of the $120-a-bottle champagne in the hopes she will request it, according to Paul Di Chiara, the cellar master.