University of Sydney Algebra Seminar

Hans Wenzl (University of California - San Diego)

Friday 17 November, 12-1pm, Place: Carslaw 375

Centralizer algebras for spin representations

Let $U$ be the semi-direct product of the quantum group $U_q({\mathfrak{so}}_{2k})$ with ${\mathbb{Z}}_2$, where the ${\mathbb{Z}}_2$ action is given via the graph automorphism on $D_k$. Let $S$ be the spinor representation of $U$. Then there exist actions of $U$ and of the non-standard $q$-deformation of ${\mathfrak{so}}_n$ on $S^{\otimes n}$ which generate each others commutants. A similar statement also holds for $U_q(s{o}_N)$ with $N$ odd.