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Homework Help: Question about spinors and gamma-matrices

  1. Jan 24, 2010 #1
    I'm working on a realisation of an exceptional group. I'm having some troubles with spinors. Here goes:

    Given a Weyl-spinor of so(6,6) (let's say the chiral one). Under the decomposition of so(6,6) into so(5,5) + u(1), what does the spinor split into? Two different Weyl-spinors (of so(5,5)) of the same chirality or two spinors of opposite chirality?

    I tried to use LiE to compute the branching rule for the spinor of so(6,6) to so(5,5) + u(1) but it did not work since so(5,5) + u(1) is not a maximal subalgebra of so(6,6). Maybe someone knows how to compute branchings into other than maximal subalgebras in LiE?

    Does anyone have a good reference on gamma-/sigma-matrices? I would like a general treatment for arbitrary signature and dimension.

    Thanks in advance,
  2. jcsd
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