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Harmonic Analysis and Special Functions on Symmetric Spaces

By (author) Gerrit Heckman, By (author) Henrik Schlichtkrull

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This text is derived from lecture notes for the European School of Group Theory, a forum providing high-level courses on recent developments in group theory. The topic is elaborated with statements of definitions and theorems; these in turn are augmented with examples. The authors extend the ideas of harmonic analysis on semisimple symmetric spaces to embrace the theory of hypergeometric and spherical functions to show that the K-variant Eisenstein integrals for G/H are hypergeometric functions under this theory. They lead readers from the fundamentals of semisimple symmetric spaces of G/H to the frontier, including generalization, to the Reimannian case.

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