Results from a partial-wave analysis of the reaction $gamma p rightarrow K^+ Lambda$ are presented. The reaction is dominated by the $S_{11}(1650)$ and $P_{13}(1720)$ resonances at low energies and by $P_{13}(1900)$ at higher energies. There are small contributions from all amplitudes up to and including $G_{17}$, with $F_{17}$ necessary for obtaining a good fit of several of the spin observables. We find evidence for $P_{11}$(1880), $D_{13}$(2120), and $D_{15}$(2080) resonances, as well as a possible $F_{17}$ resonance near 2300 MeV, which is expected from quark-model predictions. Some predictions for $gamma n to K^0 Lambda$ are also included.
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