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Representations of Brauer category and categorification

报告题目:Representations of Brauer category and categorification

邀请人:殷允川

报告人:宋林亮 副教授 同济大学
时间:2019年124日(周三) 16:00-17:00
地点:红瓦楼723
摘要:We study representations of the locally unital and locally finite  dimensional  algebra $B$ associated to the Brauer category with defining parameter $\omega_0$ over an arbitrary field $\kappa$ with  characteristic $p\neq 2$.  Let $B$-Mod be the category of all locally unital $B$-modules. We show that $B$-Mod is a standardly stratified  category in the sense of Losev and Webster. The Grothendieck group $K_0(B\text{-Mod}^\Delta)$ will be used to categorify  the integrable highest weight $\mathfrak {sl}_{\kappa}$-module $ V(\varpi_{\frac{\omega_0-1}{2}})$ with the fundamental weight $\varpi_{\frac{\omega_0-1}{2}}$ as its highest weight, where $B$-Mod$^\Delta$ is a subcategory of $B$-Mod in which each object has a finite $\Delta$-flag, and $\mathfrak {sl}_{\kappa}$ is either  $\mathfrak{sl}_\infty$ or $\hat{\mathfrak{sl}}_p$ depending on whether  $p=0$ or $ p>2$. As $\mathfrak g$-modules, $\mathbb C\otimes_{\mathbb Z} K_0(B\text{-Mod}^\Delta)$ is isomorphic to $ V(\varpi_{\frac{\omega_0-1}{2}})$, where $\mathfrak g$ is a Lie subalgebra of $\mathfrak {sl}_{\kappa}$. This is a joint work work with Hebing Rui. 
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