image/svg+xml Plan: Part 1: The objectsPart 2: The philosophyPart 3: The construction Part 1: The objects This talk is about nilpotent Gelfand pairs. What are Gelfand pairs? Why are Gelfand pairs useful? How? What are nilpotent Gelfand pairs? Nilpotent Gelfand pairs have been classified. (Vinberg, Yakimova) Why? In certain settings it works beautifully: (Kirillov '61,'62) N simply connected nilpotent Lie group