The New York Youth Symphony began its Carnegie Hall concert Sunday afternoon with ''American Slick,'' a work by the young composer William Doerrfeld, who said in a program note that he ''set out with one thing in mind . . . to make the orchestra boogie.'' That he does, in loud-louder-loudest terms that leave this observer inclined to wait and hear what other arrows Mr. Doerrfeld has in his quiver before offering an opinion on his abilities.
The best part of the program went in an opposite direction: the Vaughan Williams ''Fantasia on a Theme by Thomas Tallis,'' led by the orchestra's assistant conductor, Peter Rubardt. His approach was cautious and earnest, but he had a clear idea of the string sound he wanted, and the concentration to mold it. And the idea was good: full, spacious, not too ripe, shimmeringly still at piano, not too dug-in at forte.
The main conductor, David Alan Miller, led a lucid, cool, deft sounding of Stravinsky's ''Symphonies for Wind Instruments'' and brought unagressive breadth to Dvorak's Symphony No. 8 in G. The first two movements of this work are especially testing for the orchestra's solo players, and yes, there were some nervous goofs (the concertmaster in particular gave the impression of not being in his best form). But there was also a feeling for shape and phrase, and for corporate participation in feeling, that one hopes these young players will carry with them as they move into the competitive world ahead.