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Homework Help: Show that two representations of permutations from S3 are irreducible

  1. Oct 15, 2013 #1
    1. The problem statement, all variables and given/known data
    Hey everyone,

    Let's consider the group S3. We have the following permutations from this group:
    [itex]\sigma_{2}=(12)(3), \sigma_{5}=(1,2,3)[/itex]

    In a two dimensional representation, the matrices for these two permutations are:
    http://imageshack.com/a/img543/160/xr2r.jpg [Broken]

    I need to show that this representation is irreducible; that there are no proper invariant subspaces.

    2. Relevant equations
    None that I know of

    3. The attempt at a solution
    No idea! I need serious help with this one!!
    Last edited by a moderator: May 6, 2017
  2. jcsd
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