A flag of a finite dimensional vector space V is a nested sequence of subspaces
of V . The symplectic group of V acts on the set of flags of V . We classify the
orbits of this action by defining the incidence matrix of a flag of V and show-
ing that two flags are in the same orbit precisely when they have the same
incidence matrix. We give a formula for the number of orbits of a certain
type and discuss how to list the incidence matrices of all orbits. In the case
in which V is a vector space over a finite field, we discuss the permutation
representations of the symplectic group of V corresponding to these orbits.
For the case in which V = (F_q)^4 , we compute the conjugacy classes of the sym-
plectic group of V and the values of the characters of the previously discussed
permutation representations. / Mathematics
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/1857 |
| Date | 06 1900 |
| Creators | Miersma, Jonathan |
| Contributors | Cliff, Gerald (Mathematical and Statistical Sciences), Kuttler, Jochen (Mathematical and Statistical Sciences), Stewart, Lorna (Computing Science) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 957192 bytes, application/pdf |
Page generated in 0.0019 seconds