Incidence homology for the hyperoctahedral group

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.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of East Anglia

Year dc:date.issued

2012

Author dc:creator

• Summers, Ben

Language dc:language

en