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本文讨论一种q畸变振子系统在畸变参数q为实数或k次单位根时的SUq(2)及SUq(1,1)对称性,并指出当k为不同值时,q畸变振子具有非玻色型激发,特别地,当k=4和6时,q振子的激发是费密型的和2阶仲费密型的,本文指出文献[6]中的部分结论是平庸的。The q-oscillator is studied in the case of q being roots of unity, and SUq(2) and SUq(1, 1), the algebras realized through the oscillators are indicated. The excitations are found to be non-bosonic and the classical mechanical counterparts are given. Especially when rank k is 4 and 6, the excitations are shown to be fermi and parafermi like respectively. Short comment upon [6] is given to show that parts of the results therein are trivial.
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