University of Sydney Algebra Seminar

Ying Xu (University of Sydney)

Friday 8 September, 12-1pm, Place: Carslaw 375

Drinfeld realisation and highest weight representations of $U_q(\mathfrak{osp}(1|2n{)}^{(1)})$

The Drinfeld realisation of a quantum affine algebra is a quantum analogue of the loop algebra realisation of an affine Lie algebra. In this talk, we will first develop the Drinfeld realisations of quantum affine superalgebras $U_q(\mathfrak{osp}(1|2n{)}^{(1)})$. This makes essential use of the notation of "Quantum correspondences". Then, by using the Drinfeld realisations, we will discuss the vertex operators for the level 1 irreducible integrable highest weight representations and the finite dimensional irreducible representations of $U_q(\mathfrak{osp}(1|2n{)}^{(1)})$. This is joint work with Ruibin Zhang.