月曜解析セミナー： A quantization of the Vershik-Kerov theory and q-Central probability measures

開催日時

2018年11月5日 16時30分 ～ 2018年11月5日 17時30分

場所

理学部3号館210

講演者

佐藤 僚亮（九州大学）

In early eighties, Vershik and Kerov studied extremal characters of the infinite-dimensional unitary group. Their main idea was to correspond extremal characters to what is called central probability measures on the paths on the Gelfand-Tsetlin graph. On the other hand, Gorin provided a quantization of central probability measures and investigated them. However, it was not know that whether these quantized central probability measures are related to some kind of characters of a certain algebraic object. In this talk, we firstly propose a quantization of Vershik-Kerov theory as a natural character theory of inductive system of compact quantum groups. Secondly, we show that these quantized characters corresponds to Gorin’s q-central probability measures when given compact quantum groups coincide with quantum unitary groups. Finally, throughout this correspondence, we show that extremal q-central probability measures coincide with ergodic ones with respect to a certain measurable group action.