They came out on stage in groups, painstakingly primped so the critics would forget-them-not. The budding genius who brought them proudly introduced one and all to the audience. It was their first time before the footlights, their first time appearing together, their big moment before the top talent in the field.

"A nice clean look," commented Ken Linkiewich into his microphone, introducing one with special pride. "Like it?" he asked the audience.

"Love it!" a voice called out from the second row.

Applause greeted each introduction. Around noon, Linkiewich announced, "This is it -- finale!" and a standing ovation met the curtain-closer -- four bright purple alliums mingled gently with pink-mink protea.

Floral designers, you see, think footlights are good for flowers, too.

Since Saturday, they've been presenting their work at an apt location -- the Mayflower Hotel -- sharing design ideas at a national symposium organized by the American Institute of Floral Designers. Yesterday morning in the State Room, Linkiewich displayed some of the creations that won him a 1980 "Florist of the Year" competition in his native Canada.

"Just something nice, loose, and airy, very comfortable, very contemporary," was the way Linkiewich described one arrangement. Just back from Copenhagen, he informed the 150 or so early-risers that no less than Hans Christian Andersen had arranged flowers when not writing fairy tales. A Danish floral designer recently re-created some of the Andersen works. One of Linkiewich's pieces showed that influence. He apologized for nature's failure to pull its weight in the piece.

"Some very bad looking carnations," he admitted, surveying it. "Please don't look close at them -- I needed the color." A shake of the head. "Too bad we're not doing a funeral workshop after this."

Throughout Linkiewich's show, Frankie Shelton, director of a school of floral design in Houston and a grande dame of the profession, provided commentary on another mike. Dendrobium orchids in her hair and a never-wilting smile on her face, she smelled a winner.

"I must say, you're a daring young man," Shelton sighed as one piece came out, its fully extended blossoms aided, according to Linkiewich, by nourishment from ginger ale. "Look at the thrust of that arrangement."

Although there are some 30,000 florist shops in the U.S., the 271 registered participants at the symposium represented the artsier side of the profession, not mere petal pushers. "More than half of them are owners, too," said David Hope of Washington's Flower Gallery, "but the association is strictly for designers." "The business basically began as a funeral business," added Herb Mitchell, outgoing national president of the institute. b"Some 80 percent of it revolved around funerals."

Funerals still account for a large part of business, which accounts for Eulalah Overmeyer's reaction when asked about requests by family members of the deceased to substitute charitable contributions for flowers.

"It's like putting a knife in my heart, cutting my throat," said Overmeyer, a vice president of American Floral Services, an industry organization. She's not against charitable contributions, but no funeral, she thinks, should be without flowers.

Nowadays, floral design is more than business. There are even professors of floral design, such as Ralph Null, who teaches in Mississippi State University's department of Horticulture. Classic books were written on floral design by the late Buddy Benz, an active member of the institute.

Despite the newfound academic respectabiltity, few floral designers get wealthy from their work. Neither are they kids tugging on their parents' shirts, telling them they want to be floral designers when they grow up. But Null says the discipline increasingly attracts students who want to combine their interest in art and plants.

For most of today, the dazzling arrangements of silk deliphinium blues, astrameria blossoms and other more spellable wonders of nature will be displayed in the Mayflower's lobby. Yesterday, many of the visiting designers, who came from overseas as well as from this country, prepared their pieces in reception rooms that began to resemble garden nurseries. While designer Benny Freeman of West Palm Beach fought his allergy to crysanthemums nearby, Mr. Juzaburo Sekiye and assistants stood as a reminder of just how respectable and culturally important floral design can be -- even without highfalutin flowers.

As his American commentator watched closely, Sekiye directed the final touches on an imitation landscape partly constructed out of potatoes (rocks) and noodles (running water). An example of Gee Caw Moe Rae, a 6,000-year-old art form, the landscape on a Mayflower serving tray would shortly join an uncannily detailed piece re-creating Migimi Island in Japan. All it awaited, the commentator said, were some carrots.