半自由正交群的不变量
Invariants of the half-liberated orthogonal group
摘要：
半自由的正交群$O_n^*$作为中间量子群出现在正交群$O_n$和它的自由形式$O_n^+$之间。我们在这里讨论它的基本代数性质，我们分类它的不可约表示。利用$O_n^*$和$U_n$之间的某种扭曲型关系、对$O_n^*$起权格作用的非交换离散群以及受李代数理论启发的一些方法，对表示进行了分类.我们利用这些结果证明了与$O_n^*$对偶的离散量子群具有多项式增长。
英文摘要：
The half-liberated orthogonal group $O_n^*$ appears as intermediate quantum group between the orthogonal group $O_n$, and its free version $O_n^+$. We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between $O_n^*$ and $U_n$, a non abelian discrete group playing the role of weight lattice for $O_n^*$, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that the discrete quantum group dual to $O_n^*$ has polynomial growth.
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