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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