Isoparity and Simple Lie Group

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Abstract
The direct generalization of the isoparity (or G‐parity), with the defining property that it is commutable with the referring internal symmetry group, is investigated on the basis of the theory of Lie algebra. This is one special problem of the group extension of a simple Lie group by an involution. It is shown that the isoparity of this type can be defined for the simple Lie groups SU(2)(A1 type), SO(2l + 1)(Bl, l ≥ 2), Sp(2l)(Cl, l ≥ 2), SO(2l)(Dl, l ≥ 3), G2, F4, E7, and E8, but not for the SU(l + 1)(Al, l ≥ 2). The relation between the inner automorphism group and the Weyl group of the simple Lie algebra concerned is available to construct the isoparity operator explicitly. Some illustrative examples are presented.

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