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Séminaire Lotharingien de Combinatoire, B52g (2004), 17 pp.

# Alun O. Morris and Patrick Mwamba

# Macdonald Representations of Complex Reflection Groups

**Abstract.**
I G Macdonald (1972) introduced a unified approach to give many irreducible representations
of Weyl groups in terms of their root systems. This generalised to Weyl groups the earlier
well known constructions based on Young tableaux due to W Specht. These were interpreted
in terms of positive systems of subsystems of root systems.
A M Cohen (1976) extended the idea of root systems to complex reflection groups
giving explicitly root systems for all dimensions greater than two.
M C Hughes (1980) had further extended his ideas to generalise the concepts of subsystems
and positive systems. These are now used to construct some irreducible representations
of complex reflection groups.

Received: November 7, 2004.
Accepted: November 22, 2004.

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