Rich with wry quotations and overlapping puns, the $9 million Arthur M. Sackler Museum at Harvard University, which was dedicated today, is as lively and elusive a new museum building as America has seen.

Its unexpected colors -- lavender and orange, graphite-gray and brilliant key-lime green -- suggest "Miami Vice." Its oddly scattered windows -- round and square and broad and thin -- slide along its striped facade like boxes on conveyor belts. The spirit of its service yard enclosed in chain-link fencing is, so says the architect, "1950s functional." But its monumental entrance way evokes archaic Greece, specifically the ancient Lion Gate at Mycenae. Two tall concrete columns, with painted ventilation vents, stand guard at the door like giant green-eyed beasts.

James Stirling, the hugely gifted British architect responsible, is a plump and jolly figure in black suede shoes and purple socks. He says, "Of course, it is no longer possible to do Classicism straight."

Stirling has built at Oxford and at Cambridge. His New State Gallery in Stuttgart, West Germany, completed last year, is among the most admired new museums of our day. He has won both the Gold Medal of the Royal Institute of Architects and the $100,000 Pritzker Prize.

He likes grand ascending stairs that seem to lead to nowhere -- one, of 60 bluestone steps, is the startling skylit spine of his new museum. He likes terra-cotta columns that slide out from under the lintels they support. He likes details that look intentionally unfinished. The "lions" at the door appear to wear punk haircuts. The eight steel reinforcing bars that stick out of their heads may someday support -- if the Cambridge City Council ever grants assent -- a 150-foot-long bridge connecting the new Sackler to the older Fogg Museum across the street. He likes buildings that, like watches, have cases that are bland and smooth, insides that are jewel bright and cunningly contrived, and formal public faces. The Sackler, whose primary donor, publisher and experimental psychiatrist Arthur M. Sackler, has also donated $4 million and a $50 million collection of Oriental art to a new museum under construction on the Mall in Washington, has, quite literally, a face. It is an Ozymandian countenance, and "eastern or antique gaze," says Sterling, "ambiguous as to origin, not exactly a western face."

The architect, it is clear, is a man in touch with ironies. But the major irony attending the completion of the Sackler is not apparent in its architecture. The complicated building, conceived 10 years ago, may never fulfil perhaps the major function for which it was intended -- the training of specialists to run America's museums.

A bitter battle is being waged today in Harvard's art museums. It is a battle of ideologies, of politics, of the left against the right.

The battle also touches on the so-called "Fogg Tradition," a tradition that for generations stressed hands-on connoisseurship, a tradition that the 100,000 works of art in the university's museums were assembled to extend.

A remarkable number of America's museum directors were trained at Harvard in this tradition, including J. Carter Brown, director of the National Gallery of Art; John Wilmerding, his deputy; and Sydney J. Freedberg, once a Fogg professor, now the gallery's chief curator. So was Philippe de Montebello, the director of the Metropolitan Museum of Art. So were Anne d'Harnoncourt of the Philadelphia Museum of Art, Evan Turner of the Cleveland and Earl A. (Rusty) Powell of the Los Angeles County Museum of Art. So, too, were the directors of the museums in Dallas, St. Louis, Minneapolis and Detroit.

The tradition that produced them took a century to develop. It paid but slight attention to the complex social forces, economic and political, that works of art might illustrate, to concentrate instead on the evanescent esthetic messages that the greatest works of art convey. The Fogg did not attempt to train historians of society. The Fogg developed taste.

It stressed, above all else, subtle connoisseurship. While students in lecture halls or libraries studied photographs or slides at other universities, at the Fogg they worked with objects, Raphaels and Ruisdaels, Rembrandts and Mark Rothkos in the university's possession. And doing so they linked themselves -- through such Harvard estheticians as Freedberg, the Mongan sisters, back through Paul J. Sachs (the banker -- connoisseur who helped build the Georgian Fogg Museum in 1927), back through Bernard Berenson to the dim prephotographic past. It was as if the Carter Browns of nowadays were linked by a kind of apostolic succession to the Walter Paters and John Ruskins of a century ago.

But as whispered conversations at this week's Sackler ceremonies made abundantly apparent, those days are now over. Marxism, Semiotics, Structuralism, Radical Feminism and other ideologies have swept Harvard's fine arts department. Paul J. Sachs used to tell his students that he could not trust any art historian who did not enjoy the "pleasures of the palette."

Scholars at the Fogg once wore handmade shoes and bow ties and clothes from Saville Row. If they were not rich themselves, they spoke as if they were conversant with the wealthy who own works of art. But nowadays professors there sometimes go to classes in overalls or leather jackets.

"The sort of museum methodology in which I was instructed is no longer taught at Harvard," says Washington's Wilmerding. "As far as art history goes at Harvard, the things in the museums might as well be 1,000 miles away," says one Philadelphia curator.

Estheticism no longer rules the classrooms at the Fogg.

Yesterday's initial lecture was given by S. Dillon Ripley, who worked in Cambridge and later spent 20 years as secretary of the Smithsonian Institution. He was followed to the podium by Freedberg, whose speech, "Thoughts on the University Museum," despite referring to "this great occasion," often sounded less like a hurrah than a lament.

Freedberg is well aware that it took the once-proud Fogg, in which he worked for nearly 50 years, more than three years to find its new director, Edgar Peters Bowron. Bowron, 47, formerly of the North Carolina Museum, took the job this month.

The reason, he suggested, is "the temptation to which the young art historian may be exposed to follow facile, passing fads of doctrine or method. It comes as a matter of obvious definition that art history should be the history of art . . . If there is now a divergence between the modes of art history that are mainly taught at Harvard and the unexampled resources Harvard's art museums offer . . . the difference should, as quickly as time and circumstance permit, be healed."

In conversation, Freedberg is bitter and outspoken. "The political direction the department has assumed," he says, "has become notorious. Some members of the faculty have gone so far to suggest that works of art be sold to raise museum funds -- almost as if they were a capitalist self-indulgence." He is most in disagreement with Harvard professor Tim J. Clark, a man whom he describes as "an avowed Marxist. If you work in 19th- or 20th-century art, you espouse his methodologies -- or else."

"Well, that's Sydney," said James Ackerman, who now holds the Arthur Kingsley Porter Professorship that was Freedberg's once. "I would call Sydney's view distorted. Certainly, the Sachs tradition is gone. Thank God. It was extremely phony in many ways."

"Let's keep the personal out of it," said Clark. "It is true I write of capitalism, class conflict and the bourgeoisie. But I have no interest in grayness, in indiscriminate leveling. Neither, in fact, did Marx. He was a worshipper of Greek art, a fanatic for Balzac and constantly quoting Shakespeare and Goethe."

Arthur Sackler collects Chinese archaic jades, Chinese paintings and furniture, pre-Colombian artifacts, Italian majolica, Piranesi drawings, European terra cottas and other works of art. His Harvard museum will house the university's collections of Indian, Near and Far Eastern art, and classical antiquities.

It has had a troubled history. In 1982, deciding that the funds raised for its endowment were insufficient, Harvard President Derek Bok canceled its construction to a fire storm of outrage. Harvard professor Seymour Slive, the project's major champion, had to raise $3 million in three weeks to put the Sackler back on track.

Though monies are still short, Bowron says that Bok has assured him that the university would meet its museum's deficits well into the '90s -- "otherwise I wouldn't have taken the job."