Flag actions and representations of the symplectic group

• Author / Creator

  Miersma, Jonathan

• 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.

• Subjects / Keywords

  • Sp(4,q)
  • Symplectic
  • Flag
  • Representation
  • Group
  • Character
  • Action

• Graduation date

  Spring 2011

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3NG8M

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.