Incidence homology for the hyperoctahedral group

Summers, Ben (2012) Incidence homology for the hyperoctahedral group. Doctoral thesis, University of East Anglia .

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The incidence structure of the cross-polytope gives rise to certain modular representations
for the hyperoctahedral group. In this thesis we introduce and begin the study
of these natural representations. In particular we show that they satisfy a branching
rule. This branching rule is used to extract information about the representations
and underlying combinatorial objects. Amongst the information extracted is a formula
for the dimensions of the representations. This has applications in calculating
the p-rank of incidence matrices arising from the cross-polytope. We also construct
explicit generators for the representations and identify cases where the representations
are irreducible.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Zoe White
Date Deposited: 07 Feb 2014 10:30
Last Modified: 07 Feb 2014 10:30


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