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 \(U_q(so_N)\) with \(N\) odd.