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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
  • Graduation date
    2011-06
  • 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.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Supervisor / co-supervisor and their department(s)
    • Cliff, Gerald (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Stewart, Lorna (Computing Science)
    • Kuttler, Jochen (Mathematical and Statistical Sciences)