University of Sydney Algebra Seminar

Jun Hu (University of Sydney)

Friday 7 October, 12:05-12:55pm, Carslaw 175

On the annihilators of tensor space in Brauer algebras

Let \(X\in\{B,C,D\}\). If \(X=C\), then we set \(K\) to be an arbitrary field and \(V\) a \(2m\)-dimensional symplectic \(K\)-vector space; if \(X\in\{B,D\}\), then \(K\) is an arbitrary field of characteristic not equal to \(2\) and \(V\) an \(m\)-dimensional orthogonal \(K\)-vector space. Let \(B_n(-2m), B_n(m)\) be the corresponding specialized Brauer algebras. In this talk, I shall review results on the annihilators of the \(n\)-tensor space \(V^{\otimes n}\) in the algebras \(B_n(-2m), B_n(m)\). If time allows, I will also mention the quantized cases (i.e., on the specialized Birman-Murakami-Wenzl algebras).