Speaker
Description
{Abstract:}\textit{The famous Schur-Weyl duality states that the commutant of the action of
$Gl(V)$ on $V^{\otimes n}$ is generated by the obvious action of the symmetric group $S_n$
on $V^{\otimes n}$. We will first give a survey of quantum groups $U_q{\mathfrak g}$ and representations $V$,
where the commutant of the action of $U_q{\mathfrak g}$ on $V^{\otimes n}$ is (almost) generated by the braid group $B_n$.
In the case of spin representations of $U_q{{\mathfrak s}{\mathfrak o}}_N$, these braid representations are best described
in the context of another $q$-deformation $U'_q{{\mathfrak s}{\mathfrak o}}_n$ of $U{{\mathfrak s}{\mathfrak o}}_n$.
This $q$-deformation can be embedded into $U_q{\mathfrak sl}_n$ as a coideal subalgebra. It can also be used
to construct more examples of subfactors which correspond to the embedding $SO(n)\subset SU(n)$
in the classical limit $q\to 1$.}
