自由么正量子群的群的Martin边界
Martin boundaries of the duals of free unitary quantum groups
摘要：
给定一个自由酉量子群$G=A_u(F)$，其中$F$不是酉$2$ -by- $2$矩阵，我们证明了$G$关于任何$G$ - $\hat G$ -不变的、不可约的、有限范围量子随机游动的对偶的Martin边界与Vaes和Vander Vennet定义的拓扑边界一致.这可以被认为是一个量子类比的事实，即马丁边界的自由群符合空间的两端凯莱树。
英文摘要：
Given a free unitary quantum group $G=A_u(F)$, with $F$ not a unitary $2$-by-$2$ matrix, we show that the Martin boundary of the dual of $G$ with respect to any $G$-$\hat G$-invariant, irreducible, finite range quantum random walk coincides with the topological boundary defined by Vaes and Vander Vennet. This can be thought of as a quantum analogue of the fact that the Martin boundary of a free group coincides with the space of ends of its Cayley tree.
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