SEN. JAKE GARN, the chairman of the Banking, Committee, raises the question of representation on the Federal Reserve Board--and the question is valid. In January, one of the board's seven seats becomes vacant. There's been no hint that the administration has an appointment in mind, or has even given the matter much thought. Public discussion--and there's been very little--has been generally in terms of the rights and lefts of Washington politics. Sen. Garn is making a broader point.

The Federal Reserve Board is an agency of great independence and great influence--not only over the money supply but over the structure and operation of the financial industry. Most of the present seven members are professional economists who have spent much of their careers in the service of the government and of the Federal Reserve System itself. The principal exception is Frederick H. Schultz, the Florida banker whose term is now expiring. It is a board of great intellectual capacity and enormous technical sophistication. But it is also something of a mandarinate. As Sen. Garn observes, it's a pretty sound rule that a board of this sort, with broad and final authority over policy, ought to reflect a diversity of perspectives--including, perhaps, the perspectives of some of the people whose affairs it regulates.

No one wants to see people appointed to this crucial board as representatives of interest groups--of the farmers, say, or the consumers, committed to voting reflexively for fixed positions. But in a large and heterogeneous democracy, demands for participation deserve respect.

The Federal Reserve is traversing a dangerous period. Its present monetary policy is correct, but the melancholy truth is that being correct does not always protect an institution from attack. The process of working down the inflation rate is generating political dilemmas that will get increasingly uncomfortable as the next presidential election draws closer. To get the board through the next several years without serious assaults on its traditional independence will not necessarily be easy. President Reagan can reduce the danger by using the January appointment to broaden, in a useful degree, the present membership.

Where might he best look for a candidate? Under the double pressures of very high interest rates and deregulation, the financial institutions have been thrown into a state approaching revolution. Perhaps the ideal choice might be a knowledgeable banker from the West, who knows a lot of farmers but doesn't always agree with them--and who gets along well with economists.