A characterization of right coideals of quotient type and its application to classification of poisson boundaries

Reiji Tomatsu*

*この研究の対応する著者

研究成果: Article査読

36 被引用数 (Scopus)

抄録

Let be a co-amenable compact quantum group. We show that a right coideal of 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 SU q (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.

本文言語English
ページ(範囲)271-296
ページ数26
ジャーナルCommunications in Mathematical Physics
275
1
DOI
出版ステータスPublished - 2007 10
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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