Elections in India's Kashmir test relations between Muslims and Hindus

In the village of Shalimar, it is an unusual spring. A mantle of snow still caps the Himalayas. There is a nip in the air. Women are bringing in the last of the winter wheat and mustard harvest from terraced, patchwork fields.

But beneath the massive, 16th-century Chinar tree, which dominates the tiny town square, only the talk of politics fills the air.

A statewide political campaign is under way. This Sunday, Kashmir's 3.1 million voters will go to the polls to elect a legislative assembly and two members of Parliament.

Politically, the village of Shalimar - as the rest of the Vale of Kashmir - was the turf of the late Sheikh Mohammed Abdullah, the legendary ''Lion of Kashmir.'' Every conceivable tree and storefront in the village is festooned with the brilliant red flag of the sheikh's National Conference Party. Cassettes of the sheikh's speeches precede the candidates who come to call.

As a leader of the movement for independence from Britain, the sheikh dominated the Kashmir political scene for 52 years. With his death in September 1982, a void was left in Kashmiri politics which will take some time to fill. The sheikh's memory is crucial to the fortunes of the National Conference party, and much of the campaigning is based almost entirely on nostalgic links.

''If there are 3,000 people here,'' said wizened Abdul Aziz Baba of Shalimar, ''a maximum of 200 votes will go to the opposition. We'll vote for the sheikh during this election, and the next time judge how the young lad (the chief minister) is coming along.''

The ''young lad'' is the sheikh's son, Dr. Farooq Abdullah. Dubbed the ''lion cub,'' he has assumed the political mantle from his father. He cannot afford to lose more than eight seats in the state's 76-member assembly. (His National Conference Party won 47 seats in the 1977 elections under the banner of the sheikh.) And he has thus aligned himself with the firebrand Islamic leader Molvi Mohammed Farooq, who is openly calling for ''self-determination'' and a state wide plebiscite.

In an interview, Dr. Abdullah speaks of the need to unite the Muslims of Kashmir's strategically vital valley against domination by Prime Minister Indira Gandhi's Congress Party (I). ''Whether we survive with a regional concept, and whether we are able to maintain our internal autonomy within the framework of the federal structure of India,'' is the crucial issue of the election campaign, says Dr. Abdullah.

But, with only eight months of experience behind him, the elections have proved a formidable undertaking. Although there is little likelihood that the ''lion cub'' will be voted out of power, the ruling Congress Party - for the first time since independence 36 years ago - is openly challenging the Abdullah family for control of the state. Concerted electioneering by Congress has spawned a predictable backlash.

It is in Kashmir's southern Jammu region where most of the Hindus live, that the election battle is being waged most strongly. Across its flat plains and up country hills, Prime Minister Indira Gandhi is waging an indefatigable campaign. Traveling by jeep and helicopter during two visits to the state in recent days, she has lashed out at communal violence, accused the opposition National Conference Party of corruption and squandering funds, and has charged that Hindu identity is being threatened by a controversial ''resettlement bill'' by which the state government has welcomed repatriation of all Kashmiris who have fled to Pakistan.

The real danger in the long run to both Mrs. Gandhi's Congress Party and the National Conference could be the limited ascendency of political groups at the militant fringe. In Jammu, the fiery orator and former Congress legislator Bhim Singh has spearheaded, through his Panther Party, a call for the return to Kashmir's Hindu identity.

The People's Conference, an Islamic fundamentalist group, demands that the word ''secular'' be dropped from Kashmir's constitution, and be replaced by ''religious tolerance.'' And the Jamait-i-Islami, a party which spans the Muslim world, has built up a sizable following and seemingly unlimited funds, as it campaigns for a plebiscite on union with Pakistan.

Both groups, according to authoritative sources, are receiving election funds from Libya, Saudi Arabia, and Pakistan. To the credit of Iran's wily Ayatollah Khomeini, he appears to be one of the Islamic world's few fundamentalist leaders who has not become involved, even though his family, like Mrs. Gandhi's, is orginally from Kashmir.

Thus, the caldron continues to simmer. Thirty-two battalions of special security forces have been airlifted to the state by the New Delhi government to supervise Sunday's contest. Although reports of election violence have been grossly exaggerated by India's New Delhi-based press, hundreds of Kashmiris have been injured, and at least two are dead.

Perhaps the only impervious region of the state has been far-off, northeastern Ladakh, the gateway to China and locus of the start of the 1962 border war between India and China.

There the inhabitants are Tibetan Buddhists, craddled on a plateau by the Himalayas. They have only two legislative seats. According to pundits in Kashmir's capital, there appears to be no seccessionist movements in Ladakh. The enterprising Ladakhis are far too busy making sweaters and wood carvings for their blossoming tourist trade.