The Beat Generation comprised a group of artists and authors known for being vaguely anti-establishment back in the 1950s when the establishment was, for the last time, actually fashionable. Consequently, they weren't appreciated until later in life. Many prominent members went to Columbia, including Jack Kerouac, Allen Ginsberg, Lucien Carr, and Lawrence Ferlinghetti, and they did a lot of smoking and hanging out at places like The West End. They're also known simply as Beats. Kerouac himself coined the name when comparing his generation to the post-WWI "Lost Generation," saying "you know, this is a really beat generation".
They were first recognized by Columbia in 1959 at a stage reading organized by the "John Dewey Society" and held in Dodge Hall's McMillin Theater. Allen Ginsberg attended; Kerouac could not. Lionel Trilling's wife, Diana, was less than enthusiastic about the event, noting that she "took one look at the crowd and knew they would smell bad."
The university was very slow to ever officially recognize the movement.