Jun Hu (Beijing Institute of Technology), On the annihilators of tensor spaces in Brauer algebras

Abstract:

Let $X\in\{B,C,D\}$. Let $K$ be an arbitrary field if $X=C$ or an arbitrary field of characteristic not equal two if $X\in\{B,D\}$. Let $V$ be a $2m$ dimensional symplectic $K$ vector space if $X=C$; or an $m$ dimensional orthogonal $K$ vector space if $X\in\{B,D\}$. Let $B_n(-2m), B_n(m)$ be the corresponding specialized Brauer algebras. In this talk, I shall review some recent progress on the description of the annihilators of $V^{\otimes n}$ in $B_n(-2m)$ or in $B_n(m)$. If time allows I shall also talk about the quantized type $C$ case (i.e., for the specialized BMW algebra $B_n(-q^{2m+1},q)$).