Spherical Functions on a Group of p-adic Type

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia

Last update: 13 February 2014


The present volume is based on a course of lectures given at the Ramanujan Institute of Advanced Study in Mathematics at Madras in March-April 1970. In essence, it is an account of the theory of zonal spherical functions on the group of rational points of a simply-connected simple algebraic group defined over a p-adic field, relative to a suitably chosen maximal compact subgroup. However, partly in order to reduce to a minimum the mathematical prerequisites for the course, and partly in order to emphasize the formal structure of the theory, we have presented it in an axiomatic form: it turns out that the axioms of Bruhat and Tits are peculiarly well adapted to our purposes, and we have therefore used them as a basis of our exposition. Consequently, the reader need not even know the definition of an algebraic group in order to understand what is going on.

Notes and references

This is a typed version of the book Spherical Functions on a Group of p-adic Type by I. G. Macdonald, Magdalen College, University of Oxford. This book is copyright the University of Madras, Madras 5, India and was first published November 1971.

Published by the Ramanujan Institute, University of Madras, and printed at the Baptist Mission Press, 41A Acharyya Jagadish Bose Road, Calcutta 17, India.

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