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Permanent link (DOI): https://doi.org/10.7939/R3NG8M

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Flag actions and representations of the symplectic group Open Access

Descriptions

Other title
Subject/Keyword
flag
representation
Sp(4,q)
character
group
action
symplectic
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Miersma, Jonathan
Supervisor and department
Cliff, Gerald (Mathematical and Statistical Sciences)
Examining committee member and department
Stewart, Lorna (Computing Science)
Kuttler, Jochen (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2011-04-08T19:48:47Z
Graduation date
2011-06
Degree
Master of Science
Degree level
Master's
Abstract
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.
Language
English
DOI
doi:10.7939/R3NG8M
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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