# 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).