WHEN pianist Vladimir Horowitz arrived in the Soviet Union this week after an absence of 61 years, the trip was being billed by both US and Soviet officials as the most important event of the cultural exchange pact signed by President Reagan and Soviet leader Mikhail Gorbachev at their Geneva summit last year. Demand clearly exceeded supply for tickets to the two concerts Horowitz is due to give in Moscow and Leningrad during his three-week visit. The Moscow concert this Sunday will be televised via satellite in the United States.
Several Muscovites who had heard of Horowitz's arrival from Western residents expressed disappointment at not being able to acquire tickets.
The Kiev-born Horowitz, who emigrated as a 21-year-old in 1925, is not a figure who rings a bell in the mind of an average educated citizen, however. A Muscovite is more likely to have heard of exiled writer Alexander Solzhenitsyn, particularly if he is 35 or older. But Horowitz is known to Soviet music lovers through Western recordings of his recitals that have filtered into the country.
Cognoscenti have been anxious to see him, not least because they are aware of the effect on the contemporary Soviet concert scene caused by the decisions of later pianists such as Vladimir Ashkenazy and one of the top young performers, Andrei Gavrilov, to live in the West.
More than 400 of the 1,700 tickets for the concert in the capital, to be given at the Moscow Conservatory this Sunday, were on sale to the general public, and Horowitz's party has brought along more. But the lion's share appear to have gone to the Soviet elite -- Communist Party members, officials of the state television and radio network Gostelradio, and others.
In this respect Horowitz's recitals will resemble pop concerts staged in Moscow, not only by Western stars such as Elton John of Britain, but even by groups that have made little impact in the West.
The lure of foreign artists, whether outstanding or mediocre, in a country hungry for a glimpse of the Western world is sufficient to ensure such events are sellouts.
In the United States, which also seems hungry for glimpses inside the Soviet Union, CBS will televise the Moscow concert on a special two-hour edition of ``CBS News Sunday Morning,'' with Charles Kuralt (Sunday, Apr. 20, 9-11 a.m., check local listings).
Horowitz's Moscow recital repertoire opens with three sonatas by Domenico Scarlatti. He will also play two preludes by Rachmaninoff -- sure to draw an emotional response -- and other works by Mozart, Scriabin, Schubert, Liszt, and Chopin. He is performing at Leningrad's Shostakovich Hall on April 27.
Horowitz has returned to a country where music, more than any other art form, has suffered from the defections of leading personalities to the West. The steady stream of pianists, conductors, violinists, and others who have left since the 1960s have deprived the country of some of the world's best musicians and dented morale among those who have remained.
The passing of performers such as the legendary violinist David Oistrakh in 1974 and the pianist Emil Gilels last year have further depleted the ranks of the Soviet virtuosos who captured the music scene after World War II.
For the Soviet arts world, Horowitz's trip is a temporary infusion after years of talent-drain caused by defections that began with the decision of dancer Rudolf Nureyev to stay in Paris in 1961.
Even putting music to one side, the list is striking, including such names as the avant-garde theater director Yuri Lyubimov, film director Andrei Tarkovsky, and ballet dancer Mikhail Baryshnikov.
Writers such as Solzhenitsyn, Vladimir Voinovich, Joseph Brodsky, and Alexander Zinoviev have been forced out of the country, but other talents -- such as poets Bella Akhmadulina, Yevgeny Yevtushenko, and Robert Rozhdestvensky -- have remained.
The exodus of musicians tells the most depressing tale from the Soviet viewpoint. The path chosen by Ashkenazy and Gavrilov is the same one followed by deported cellist Mstislav Rostropovich and his opera singer wife, Galina Vishnevskaya, and conductors Kirill Kondrashin and Maxim Shostakovich (son of the composer).
Gidon Kremer, a pupil of Oistrakh, defected in 1980. Another star violinist, Viktoria Mullova, was celebrating her Tchaikovsky Prize triumph with a concert tour of Finland when she took a taxi ride over the Swedish border and never went back.
Those who leave usually blame the tight controls over artists exercised by party bureaucrats and the Ministry of Culture. Permission is needed for every recording, and trips abroad are accorded only to the privileged.
Defections have made Soviet authorities increasingly wary of allowing performers to go abroad, for fear they will not return.
Western diplomats who specialize in the cultural scene here detect few signs of an easing in the music field and a recent nationwide composers' congress ended with calls on composers to remember that their work must have a strong ideological content.