Several Key Rulings Will Fill High Court’s Final Days : Law: Justices have left some of the toughest cases for last. Decisions on abortion protests, the death penalty, taxes and voting rights remain.

On a Thursday afternoon in late May, the justices of the Supreme Court gathered in an ornate conference room for a music recital.

Justice Harry A. Blackmun, who had conceived the idea and invited six distinguished musicians, said he thought listening to music together would have a salutary impact on his often-combative colleagues.

The recital and the reception that followed would “increase the level of joviality among the justices at this time of year,” Blackmun commented in introducing the program.

For the high court, “this time of the year” is decision time. In the last week of May and first weeks of June, the justices must finally decide their cases, some of which have been pending since the first week in October.

Chief Justice William H. Rehnquist, a stickler for working by the clock, insists that all the opinions be ready for announcement by the last week in June. While the court has heard fewer cases during this term, it now finds itself in the usual spot--with some of the hardest cases left for last.

Here are highlights among the 35 cases still awaiting decision:

CABLE TV--Does the 1992 law that requires local cable television operators to broadcast virtually all nearby over-the-air stations violate the 1st Amendment rights of the cable companies? If the justices agree with the industry, the ruling in the case of Turner Broadcasting System Inc. vs. the Federal Communications Commission could have broad impact in the communications field.

ABORTION PICKETING--Can a judge block anti-abortion protesters from picketing and praying at the gates of an abortion clinic, or does such an order violate their free-speech rights? A ruling in the case of Madsen vs. Women’s Health Center could affect the constitutionality of the newly enacted federal law designed to protect abortion facilities.

DEATH PENALTY--Is California’s death penalty law unconstitutional because it permits jurors to consider vague factors when deciding upon a sentence of life in prison or death for a convicted killer? A ruling in Tuilaepa vs. California could affect the fate of the state’s 375 inmates on Death Row, but the justices indicated during the March arguments in the case that they are likely to uphold the law.

RELIGION--Can a state carve out a special school district to serve a separatist religious sect? If the answer is yes in this New York case, other sects are likely to seek the same benefits. But the ruling in the Village of Kiryas Joel vs. Grumet is likely to be narrowly focused and will not have a broad impact on other cases involving the separation of church and state.

UNITARY TAXES--Is California’s now-repealed unitary tax on multinational corporations unconstitutional? A loss in the case of Barclay’s Bank vs. Franchise Tax Board could cost the state as much as $4 billion, but during oral arguments, the justices sounded as though they will reject the bank’s claim.

VOTING RIGHTS--Is a state required to maximize the number of legislative seats for blacks and Latinos when drawing boundaries for voting districts? This case from Florida raises a series of complicated questions because benefiting blacks can hurt Latinos and vice versa. The justices heard arguments in Johnson vs. DeGrandy on the first Monday in October but have struggled since then to issue a decision.

SIGNS--Can a city outlaw the display of all signs and billboards, except those necessary to identify a residence or business? If the court were to rule for the city in Ladue, Mo., vs. Gilleo, officials would have far broader authority to ban billboards and other “visual clutter.”

RETROACTIVE TAXES--Can Congress repeal a tax benefit after a taxpayer has taken advantage of it and order the Internal Revenue Service to seek retroactive payments? Since the 1930s, the high court has given state and federal officials broad powers to impose retroactive taxes, but the case of U.S. vs. Carlton has forced the justices to rethink that doctrine.

PROPERTY RIGHTS--Can city officials force a store owner to give up some of his property for use as a bike path as a condition of getting a building permit, or is that requirement an unconstitutional “taking” of private property? In a 1987 case involving a Ventura beachfront home, the high court said it would frown on a public agency’s demands that amounted to “extortion” of property owners, but the justices have been unable to agree on a clear standard.