A Characterization of Right Coideals of Quotient Type and its Application to Classification of Poisson Boundaries
A Characterization of Right Coideals of Quotient Type and its Application to Classification of Poisson Boundaries
复制标题
商型右余理想的刻画及其在泊松边界分类中的应用
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Reiji Tomatsu
中科院分区：
文献类型：
--
作者：
Reiji Tomatsu
设$${mathbb{G}}$$是一个可合作的紧量子群。我们证明了$${mathbb{G}}$$的右余理想是商型的当且仅当它是保持Haar态的条件期望的值域，并且在对偶离散量子群的左作用下是全局不变的.我们将这个结果应用到Izumi为离散量子群引入的Poisson边界理论中，并推广了Izumi-Neshveyev-Tuset关于SUq（N）的工作，使之适用于具有交换融合规则的可共守紧量子群.更精确地说，我们证明了Poisson积分是Poisson边界与商型右余理想之间通过Kac型极大量子子群的同构。特别是，泊松边界和量子旗流形是同构的任何q-变形的经典紧李群。
Let $${mathbb{G}}$$ be a co-amenable compact quantum group. We show that a right coideal of $${mathbb{G}}$$ is of quotient type if and only if it is the range of a conditional expectation preserving the Haar state and is globally invariant under the left action of the dual discrete quantum group. We apply this result to the theory of Poisson boundaries introduced by Izumi for discrete quantum groups and generalize a work of Izumi-Neshveyev-Tuset on SUq(N) for co-amenable compact quantum groups with the commutative fusion rules. More precisely, we prove that the Poisson integral is an isomorphism between the Poisson boundary and the right coideal of quotient type by a maximal quantum subgroup of Kac type. In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group.