King Oliver, Jelly Roll Morton, Fats Waller, Louis Armstrong, Sidney Bechet and Duke Ellington are alive and swinging in the capable hands of the Smithsonian Jazz Repertory Company. If vocalist Alberta Hunter is the living tradition in the Smithsonian's 10th anniversary celebration of jazz this weekend, then the Jazz Rep is the loving tradition.

"The main idea of jazz in repertory is not just to copy old records," says Bob Wilber, leader of the 2-year-old Jazz Rep, which performs tomorrow night at Baird Auditorium. "The fact that the phonograph was invented at about the same time as jazz was a very fortunate circumstance; it has preserved essentially improvised music. What we do is go back and study the records and in many cases do actually transcribe the solos note for note. But the ideal is to develop repertory players who are able to play within the style but also put a lot of themselves into it."

Contemporary jazz may be "so abstract, difficult and complex," says Wilber, that the average listener is turned off. But he points to the 70-year-old genre's early decades as a source of inspiration. "We're getting a perspective, a chance to rediscover our past," he says. "We're getting further away in time from the jazz of the '20s, '30s,'40s and '50s. The same thing that has happened in jazz happened in modern classical music: the audiences got smaller and smaller. Most of your classical audience today wants to hear Bach, Beethoven, Brahms, Mozart. I think there's a newly developed audience that wants to hear the classics of American jazz."

The maintenance of tradition through the repertory movement is an ongoing concern for both the Smithsonian and Wilber. The now 53-year-old clarinetist, saxophonist and arranger was something of an anachronism when he surfaced in the bop-oriented '40s. He arrived with a traditional sound grounded in the work of jazz giants two decades before. "I was also very interested, and still am, in new developments," says Wilber, "but I feel the need of keeping the tradition alive."

Wilber, who holds degrees from both the Eastman and Juilliard Schools of Music and pursues a part-time classical career, also studied with the legendary soprano saxophonist Sidney Bechet for two years in the '40s, learning "the importance of communicating with an audience the idea that jazz was more than just notes and rhythms, that it was a tradition . . . that this music would die unless it was passed on."

Like most jazz players, Wilber went through a long grounding period as a soloist and arranger for different combos and orchestras (his best known groups being the World's Greatest Jazz Band and Soprano Summit in the '70s). In 1976, he was a founding member of the New York Jazz Repertory, a floating group of musicians dedicated to the idea of maintaining a classic jazz book.

He says that "it's difficult for young players to learn how to swing. The swing in jazz had a lot to do with the fact that jazz was a dance music with a tremendous interaction between dancers and musicians. Today, jazz has become a concert music. It's much easier when you have people responding to you with their bodies."

The eight carefully selected players in the Smithsonian's Rep have to improvise and think in styles ranging from New Orleans to contemporary.

The Smithsonian Jazz Rep, which winds up the institution's jazz celebration with a concert tomorrow night, does three major tours each year. "We're reaching outside the jazz audience, trying to broaden the audience for this kind of music," Wilber says. The company has just finished a recreation of the King Oliver Creole Jazz Band, "the most influential jazz band of the early '20s. We transcribed from early acoustical recordings, and it was hard trying to figure out what everybody played."