國立清華大學 數學系

Abstract In this talk, we will first recall the celebrated Schur-Weyl duality, which connects the representation theory of type A Lie algebra and that of the symmetric group. Then we will mention some of its variations to other classical Lie algebras or Lie superalgebras, which leads to the discovery of some interesting algebra structures including the well-known Brauer algebra. In particular, we will introduce a new algebra $\hat P_d^-$, called the {\it affine periplectic Brauer algebra}. This algebra can be defined by generators and relations that are very similar to those of the degenerate affine Nazarov-Wenzl algebra except for some crucial signs. One can also describe $\hat P_d^-$ as a diagram algebra similar to the case of the Brauer algebras. This talk is based on joint work with Chih-Whi Chen.