Symmetric functions and Hall polynomials (1979, much extended second edition in 1995) is a standard reference book about the representation theory of the symmetric group and its many combinatorical, algebraic and group theoretical applications. In Affine root systems and Dedekind's eta-function (Inventiones Mathematicae 15, 1972) he establishes a connection between a number theoretical observation by the physicist Freeman Dyson and the theory of simple Lie algebras. In Some conjectures for root systems (SIAM Journal on Mathematical Analysis 13, 1982) Macdonald formulates some conjectures about the combinatorical properties of so-called root systems. In 1987/88 he defines a class of symmetric functions, and more generally a class of polynomials associated with root systems, which are now both known as Macdonald polynomials (see A new class of symmetric functions and Orthogonal polynomials associated with root systems in Séminaire Lotharingien Combinatoire 20, 1988 and 45, 2000). The impact of these polynomials, both in mathematics and in theoretical physics, has been enormous.
Ian Macdonald started his scientific career in 1957 as a lecturer in mathematics at the University of Manchester. Until his retirement in 1987 Macdonald has worked during many years as a professor at Queen Mary College in London. Since his retirement he has remained active in research with publications and lectures.
See a list of all honorary doctorates granted by UvA to mathematicians.