Gel'Fand, Graev, and Vilenkin originally intended the material on the theory of representations to be in some chapters in the fourth of five volumes, but decided to add a volume devoted to it entirely. They find that representation theory is based on what they call integral geometry, that is, geometry that involves the transition from functions defined on one set of geometrical objects--for example on the points of some linear surface--to functions defined on some other set--for instance on the lines generating this surface. They accomplish the transition from one space to the other with the simultaneous transformation of the function defined on it. Annotation �2016 Ringgold, Inc., Portland, OR (protoview.com)

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