Elizabeth Taylor sent Sen. John Warner, her most recent running mate, tickets to see her romp through "Private Lives" at the Kennedy Center last Saturday.

Warner, the senior senator from Virginia, brought his mother, Martha Budd Warner, to watch his former wife cavort on stage with one of her former husbands, Richard Burton.

Apparently the Warners enjoyed the play, with all its too-good-to-be-true lines about marriage. And they came backstage after the performance to visit Taylor.

Sunday night, Taylor played audience herself when she slipped into Al Pacino's "American Buffalo," playing the Terrace Theater. The two stars are old friends; they were introduced by a bodyguard who has worked for both of them.

Pacino says "don't tell me" if a friend is in the audience. So Taylor hid in a nearby office during intermission and sat on a side of the house away from Pacino's stage position. After the performance, Taylor went backstage for hugs and kisses and congratulations.

Meanwhile, Taylor's own play brought in half a million dollars in ticket sales last week, according to Michael Lonergan, the company manager--a record, he said, for a play in the Opera House.

Alvin the Parrot, according to Lonergan, has not let success go to his head. "He's still the same bird he's always been. Nothing flighty about him. As a matter of fact, he doesn't fly--just waddles about."

Alvin, however, has his fans. Albert Taxin, owner of the waterfront Bookbinder's restaurant in Philadelphia, sent Alvin two pounds of bird seed, "and the smallest size of our Original Bookbinder's T-shirt." Taxin said, "Everybody was sending Elizabeth food, I thought Alvin should have something, too." Taxin said he didn't see the actress when she was in Philadelphia with "Private Lives"--"though she's eaten with us many times before."

The other Bookbinder's in Philadelphia, the one on Walnut Street owned by the original Bookbinder family, said it sent Taylor lunch every day while she was in Philadelphia. "She always ordered the low-calorie Dover sole. I convinced her to try the pompano one day, but she didn't like it," said Sam Bookbinder. One day, after many lunches of fish, Bookbinder said, "she called up for the name of a good Jewish delicatessen where she could get a proper hot pastrami."