Homology representations of unitary reflection groups
This paper continues the study of the poset of eigenspaces of elements of a unitary reflection group (for a fixed eigenvalue), which was commenced in  and . The emphasis in this paper is on the representation theory of unitary reflection groups. The main tool is the theory of poset extensions due to Segev and Webb ( ). The new results place the well-known representations of unitary reflection groups on the top homology of the lattice of intersections of hyperplanes into a natural family, parameterised by eigenvalue.Keywords: Poset topology, unitary reflection groups, homology representations.
AMS Subject Classification: Primary 20F55; secondary 05E18.
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