LARRY HUX, the hero of Robert Towers's first novel in 19 years, starts out as a a familiar type in contemporary fiction. In his late 30's, recently divorced, troubled by insomnia and an expanding waistline, he struggles to maintain a dapper public image while his East Side studio apartment sinks into private squalor. Hux doesn't care anymore; he's aliented from his ex-wife, his child, his job, everything. Sometimes he picks up a prostitute, but his potency is shaky. So most evenings he just sits at home, drinking beer and eating pistachios, dropping cans and shells on the floor. All this dreary stuff, however, is pushed aside on page six, when a ghost appears to Hux. Clark Helmholtz, his best friend at Princeton graduate school, is suddenly sitting on Hux's bed; blood oozes from the shotgun wound that shattered Clark's skull and killed him 10 years ago in Mississippi during the turbulent Freedom Summer of 1964. The apparition vanishes, but Hux has been summoned. Trumping up a program for the philanthropic foundation that employs him, Hux heads south, to the land of his birth. His ostensible mission is to canvass the neediness of small Missis Walter Kendrick, who teaches English at Fordham University, is the author of ''The Novel Machine: The Theory and Fiction of Anthony Trollope.'' sippi colleges, but his real focus is the little town of Alhambra, where Clark's acquitted murderer, Dr. Claiborne Herne, still lives. This sharp detour from the expected fictional path is the first of many in ''The Summoning,'' which sets up one conventional expectation after another only to deliver something surprising each time.