Abstract
For Dynkin labels of weights in 5 and 10 of SU(5), 10 and 16 of SO(10) and 27 ofE, we find it instructive to (a) explōit the Cartan decom position into a nonsemi simple symmetric subalgebra and coset space, (b) introduce a set of annihilation and creation operators, that may act on an invariant 10>, to represent suitably the shift-action and weight-vectors.
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References
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Das, T., Soni, S.K. Weights of elementary representations in SU(5)-SO(10)-E6 chain. Pramana - J. Phys. 18, 349–383 (1982). https://doi.org/10.1007/BF02879396
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DOI: https://doi.org/10.1007/BF02879396