In the final volume of the series, Gel'fand, Graev, and Pyatetskii-Shapiro continue the discussion of representation theory from Volume Five and examine automorphic functions. They begin by looking at problems of representation theory and the theory or automorphic functions connected with a Lie group and a discrete subgroup to it. Then they construct the theory of representations of the group of matrices in order Two with elements from an arbitrary locally compact topological field. They conclude with a study of the group of adeles and the natural homogeneous spaces that arise in connection with these groups. They do not assume readers to be familiar with adele groups, so provide an expository account of the basic ideas. Annotation 2016 Ringgold, Inc., Portland, OR (protoview.com)

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Text: English (translation)
Original Language: Russian

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