given a representation $v$ of a group $g$, it is a classical problem to determine the centralizer of its action on the n-th tensor power of $v$. if $v$ is the natural module of a classical lie group, this led to the famous schur-weyl and brauer-weyl dualities. in this talk, we solve this problem for the spinor representation $s$. for even-dimensional spin groups, the centralizer on the n-th tensor power of $s$ is given by a representation of $so(n)$, with a similar result also for the odd-dimensional spin groups. time permitting, we discuss generalizations of this result to quantum groups and to classification of tensor categories. please note: there will be a pre-talk for graduate 2022年亚洲世界杯预选赛 from 2:30 - 3:00. the regular talk will begin at 3:00.