The Gilded Years of the late nineteenth century were a vital and glamorous era in New York City as families of great fortune sought to demonstrate their new position by building vast Fifth Avenue mansions filled with precious objects and important painting collections and hosting elaborate fetes and balls. This is the moment of Mrs. Astor's ''Four Hundred,'' the rise of the Vanderbilts and Morgans, Maison Worth, Tiffany & Co., Duveen, and Allard. Concurrently these families became New York's first cultural philanthropists, supporting the fledgling Metropolitan Museum of Art and the Metropolitan Opera, among many institutions founded during this period. A collaboration with the Museum of the City of New York, ''Gilded New York'' examines the social and cultural history of these years, focusing on interior design and decorative arts, fashion and jewelry, and the publications that were the progenitors of today's shelter magazines.