## Spherical Functions on a Group of $p\text{-adic}$ Type

Last update: 13 February 2014

## Preface

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 $p\text{-adic}$ 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 $p\text{-adic}$ 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.