Geodesic
Macdonald Representations of Complex Reflection Groups
Séminaire lotharingien de combinatoire, Tome 52 (2004-2007)

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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. 

@article{SLC_2004-2007_52_a6,
     author = {Alun O. Morris and Patrick Mwamba},
     title = {Macdonald {Representations} of {Complex} {Reflection} {Groups}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {52},
     year = {2004-2007},
     url = {http://geodesic.mathdoc.fr/item/SLC_2004-2007_52_a6/}
}
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Alun O. Morris; Patrick Mwamba. Macdonald Representations of Complex Reflection Groups. Séminaire lotharingien de combinatoire, Tome 52 (2004-2007). http://geodesic.mathdoc.fr/item/SLC_2004-2007_52_a6/