No palm tree grows in Brooklyn, and somehow the one looming over the right field stands here just doesn't look right. After all, these are the Dodgers, and even if they are in the city of the angels, they'll always be the Brooklyn Dodgers to any self-respecting Yankee fan. The image of Duke Snyder dislodging a coconut with a long shot is pure surrealism.

Almost as surrealistic as Linda Ronstadt singing the National Anthem at Friday's game. Forget about Jose Felociano, and the big stink he caused a few years back when he bossanovafied the bombs bursting in air. Nothing of the sort from Ronstadt. The doyenne of Southern California rock 'n' roll simply belted it out, show-big biz perfect.

In fact, snow biz seems to be what Dodger baseball is all about these days, a far cry from the two classic Yankee-Dodger subway series in the '50s. This is California, land of the body beautiful. So what better form os show business can there be than televised athletics?

The night that catcher Steve Yaeger got hit in the crotch with a foul tip, the local female newscaster closed the show with, "Steve, all the girls here hope it doesn't happen again." That's entertainment.

The most famous person at Dodgers' stadium is a high-school teacher who moonlights selling peanuts at the park. Every fan knows him by name because he's been interviewed on television and writtern about more than Dusty Baker. The guy is a celebrity: tossing bags down long aisles with fast-ball accuracy and then catching the quarters that come winging back. He gets mobbed by fans, and can move $200 worth of peanuts in a night.

Then there are the real celebrities in the stands: this movie star and that television actor being flashed on the TV screen from their boxes behind the Dodger dugout. You see them driving up outside the stadium: the Mercedeses and Rollses dropped them at the gate and then their chauffeurs hook portable TVs up to the cigarette lighters and watch the game out in the lot.

Inside the place looks like a huge casting call. With the exception of a few die-hard fans - mos of them are ready for the Yanks - almost everybody is dressed to the nines: women in a very proper and very slinky evening wear; men in tuxedos; 5,000 Farrah Fawcett-Majors haircuts; absolutely nobody lugging a mitt around in hopes of shagging a foul.

Mornings in the lobby of the Biltmore Hotel, where the World Series entourage (minus the Yanks) is staying, it looks like the floor of the New York Stock Exchange. Hundreds of people mob the place. Men carrying leather briefcases are wandering around, scalping tickets at $75 to $100 apiece. Other men are rushing to banks of phones: "We got you two in the loge; will you take two more in the upper deck?" Sportswriters who haven't seen each other since last year's series palling around; a few poncho PR men are greeting people in that lobby; and a bellboy is jumping up and down because he's just been given a ticket as a tip .

But the real action is over at the Hilton, where the Yankees are staying. This makes scenes at Hotels hosting rock stars seem limp in comparison. There must be 100 women - from 16-year-old nymphettes just in from the latest Kiss tour to 300-pound potato chip munchers - stalking the fllor, waiting for just one glimpse at a world champion New York Yankee.

Little of this enthusiasm really crept into the park on Friday, except during the celebrated Dodger seventh-inning stretch. Granted, the crowd went bananas when Baker slammed a three- run homer into the left-field seats. But when the park announcer enjoined the fans to rise and sing "Take Me Out to the Ball Game," it was pure show biz. You absolutely knew that every person still sitting was a fanatic Yankee rooter. The words flashed on the electronic score board, and the strains of "Root, root, root for the Dodger's," circled their way up to mingle with the smog.

By the bottom of the eighth, the aisles were packed with despondent Dodgers fans heading for their cars. The game had not been very show biz, which is to say it had a weak ending.

Not to mention, as one Yankee fan pointed our, that everybody had to rush home and watch "Charlie's Angels."