LIBYAN protesters want the political authorities to quit and hold elections after previous transitional periods created institutions that clung on long after their mandates expired. Here are Libya's main political institutions that have so far failed to overcome entrenched differences between rival authorities in the east and west of the country, a divide that emerged after the 2011 toppling of autocrat Muammar Gaddafi. HOUSE OF REPRESENTATIVES Libya's House of Representatives was elected in 2014 as the national parliament with a four-year mandate to oversee a transition to a new constitution prepared by another elected body. But the legitimacy of the…