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When the New York City Ballet pulls up to the Kennedy Center this week, they’ll be hauling more than five decades of ballet nostalgia with them. Led by Peter Martins, the company performs two programs during their stay. The first pays tribute to City Ballet’s first ballet master, George Balanchine, featuring his choreography for Swan Lake, Allegro Brillante, and Tchaikovsky Suite No. 3. While that program is as traditional as a strand of pearls, its companion has a bit more contemporary razzle dazzle, featuring Christopher Wheeldon’s Carousel (A Dance), Jerome Robbins’ Glass Pieces (set to the music of Philip Glass), and Balanchine’s Vienna Waltz. If Swan Lake’s dancing waterfowl don’t hold your interest, consider the more modern Allegro Brillante, which Balanchine said contains “everything I know about classical ballet in 13 minutes.”

The New York City Ballet performs Friday at 7:30 p.m., Saturday at 1:30 p.m. and 7:30 p.m., and Sunday at 1:30 p.m. at the Kennedy Center Opera House, 2700 F St. NW. $25–$95. (202) 467-4600. kennedy-center.org.