Monday Analysis Seminar: A quantization of the VershikKerov theory and qCentral probability measures
 Date

2018115 16:30 
2018115 17:30
 Place
 Faculty of Science Building #3 Room 210

Speaker/Organizer
 Ryosuke Sato (Kyushu University)

 In early eighties, Vershik and Kerov studied extremal characters of the infinitedimensional unitary group. Their main idea was to correspond extremal characters to what is called central probability measures on the paths on the GelfandTsetlin 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 VershikKerov theory as a natural character theory of inductive system of compact quantum groups. Secondly, we show that these quantized characters corresponds to Gorin's qcentral probability measures when given compact quantum groups coincide with quantum unitary groups. Finally, throughout this correspondence, we show that extremal qcentral probability measures coincide with ergodic ones with respect to a certain measurable group action.
Place: Science Building #3 Room 210
Monday Analysis Seminar