Group representations and characters
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Abstract
In the first section of this thesis we are primarily concerned with generating a method for determining the complete set of different ordinary matrix representations of a finite group G over a field F. In order to accomplish this task we first define the notions of a matrix representation, and a representation module. We then show that every representation of G determines a representation module of G, and conversely. the decomposition of representation modules is then seen to be very important. In particular, if a representation module M decomposes into a direct sum of irreducible representation submodules, say
M=M1 + ••• +Mn,
then the associated representation p decomposes into a direct sum of irreducible representations, say
p = p1 + ... + pn,
where pi... is the representation associated with the module Mi. We then prove that this result is always true provided that the order of the group G is not divisible by the characteristic of the field F. (When the characteristic of the field divides the order of the group the representations are said to be modular, otherwise they are called ordinary.) [TRUNCATED]
Description
Thesis (M.A.)--Boston University
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PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.