United Nations, N. Y. — As the 37th General Assembly begins its work Sept. 21, the United Nations finds itself at a crossroads.
It could begin to slide rapidly down the way of the League of Nations, turn into a sterile debating society, and in the not too distant future be abolished altogether.
Or it could - with the help of a number of powerful and influential nations - retain its credibility and perhaps even see its role as a peacekeeping organization strengthened.
Conventional wisdom has it that this session will be dull, muted, and unproductive. These are the reasons:
* The UN has been ''offended and humiliated'' again in recent months because it was not allowed to play a role in preventing military confrontations in the Falklands and in Lebanon.
* The third world, which in recent years has asserted itself more and more forcefully, comes to the General Assembly without a defined strategy this year. This is because the Organization of African Unity was not able to hold its August summit and because the nonaligned nations had to postpone their own summit until next year.
* Furthermore, the third world is in general disarray. Brazil, Mexico, Indonesia, Algeria, Egypt, Zaire, Pakistan are in serious financial straits and need new loans and rescheduling of debts. Thus, they are expected to be ''realistic'' in their demands.
* North-South and East-West relations are blocked. The South is reeling under a double military defeat - Britain trounced Argentina, and Israel (considered to be a member of the West) once more defeated the Arabs. The new ''cold war'' has all but frozen East-West relations.
Most serious experts here consider at a standstill ''global negotiations'' to give poor nations economic concessions from the richer nations.
The usual items will be debated and voted on. But no new diplomatic ground is expected to be covered regarding Afghanistan, Kampuchea (Cambodia), the Western Sahara, Namibia, and the rights of the Palestinians.
On the other hand, UN Secretary-General Javier Perez de Cuellar's annual report - ''a small time bomb'' as one diplomat calls it - may yet explode and make this General Assembly a lively, useful, and perhaps crucial one.
His recent call for strengthening UN peacekeeping mechanisms and for restoring the secretary-general's role in assuring collective security may become, say to various informed sources, the central theme of the session.
There are signs that the Secretary-General's ideas will be picked up by many foreign ministers from Europe, from the communist countries, and from the third world.
''His report may turn out to be the UN's swan song or it may signal a rebirth of the UN,'' says a Western ambassador.
''While it is unrealistic to expect the Secretary-General to solve Soviet-American bilateral issues, he could be used to prevent conflicts like those which recently engulfed Lebanon and the Falklands or that oppose Iraq and Iran,'' says a source close to the Secretary-General.
Foreign ministers involved in disputes could, in private meetings around the Security Council chambers, iron out their differences.
Sixty foreign ministers and a few heads of state are expected to speak. Many are expected to speak out for strengthening the UN. This trend reportedly runs counter to the Reagan administration's wishes. US diplomacy appears to be still trying to remove serious problem-solving from the UN in favor of bilateral talks.
This inclination may of course be strengthened - for example, for first time the question of Puerto Rico will be raised at the General Assembly as a ''colonial problem.''
Cuba, which will play the part of the prosecutor on the Puerto Rico issue, may not get the necessary votes for a resolution that would embarrass the United States.
But tempers are expected to flare during that debate.
Just as it was for Hamlet, the question for the United Nations today is ''to be or not to be.''
True, Shultz and Gromyko will be meeting on Sept. 28 in New York but no breakthrough is expected to occur at this time between Washington and Moscow.
Indeed, serious statesmen might realize that the world would be the worse off , a more dangerous place to live in without the UN and might agree, if not to surrender their nations' sovereign power to the UN, then at least to use the Security Council more forcefully, according to the same source.
including Brazil's President Joao Figuereido, France's Prime Minster Pierre Mauroy, Cambodia's Prince Norodom Sihanuck.
Argentina is expected to bring up the Falklands issue in a very mild form indeed. It will simply call for renewed talks with Britain concerning the islands. This resolution is expected to be adopted by an overwhelming majority. Britain, however, is reported to be rejecting any negotiations for the time being.
The Soviet Union will be asked to leave Afghanistan but is not expected to comply. Vietnam will be directed to withdrawlet go of Cambodia but is unlikely to listen. Israel will turn its usual deaf ear to resolutions concerning the rights of the Palestinians. No progress is expected on Cypress. Neither are Iraq and Iran ready to abide by UN resolutions and bury their war hatchet.