Paris - Leila Pahlavi, the 31-year-old daughter of the late Shah of Iran, has died in London after a long period of depression, her mother, the former empress Farah, announced yesterday. She said in a statement her daughter died in her sleep on Sunday night. "For the past few years, Leila has been very depressed," the empress said. "Time had not healed her wounds. Exiled at the age of nine, she never surmounted the death of her father ... to whom she was particularly close."