1. Feb 2, 2017 #1

   arivero

   

   Gold Member

   In E6, the product 27 x 27 contains the (conjugate) 27. In SU(3), something similar happens with 3 x 3, which decomposes as 3 + 6.
   
   I was wondering, how usual is this? Do we have some lemmas telling when a product N x N is going to "recover" the original N, or its conjugate, inside the sum?

    

   arivero, Feb 2, 2017
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3. Feb 3, 2017 #2

   arivero

   

   Gold Member

   so, what happens is that R x R always decompose in a sum of the symmetric plus alternating (or exterior) square.

    

   arivero, Feb 3, 2017

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