In this note, we generalize a result of Mikkelsen–Szymański and show that, for every $n\ge 2$, any bounded ∗-representation of the quantum symplectic sphere $S_q^{4n-1}$ annihilates the first $n-1$ generators. We then classify irreducible representations of its coordinate algebra ${𝒜}(S_q^{4n-1})$.

中文翻译：

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量子辛球的坐标代数不嵌入任何 C*-代数

在本笔记中，我们概括了 Mikkelsen-Szymański 的结果并表明，对于每个 $n\ge 2$, 量子辛球的任何有界 ∗ 表示 ${秒}_q^{4n-1}$ 消灭第一个 $n-1$发电机。然后我们对其坐标代数的不可约表示进行分类${𝒜}({秒}_q^{4n-1})$.