主持人：沈耀龙
摘要：
The affine Brauer category acts naturally in representation theory of classical Lie algebras. We explain how such actions are related to 2-representations of quasi-split type AIII $\imath$-Kac--Moody 2-categories. Generalized eigenspaces of the affine Brauer dot provide the color functors. We describe the generating natural transformations in both directions using explicit diagrams, and explain the additional normalization and relation checks required at the fixed vertex 0 in the integral case. As an application, we identify the locally unital algebra associated with a cyclotomic Brauer category with that arising from the corresponding cyclotomic quotient of a principal $\imath$-Kac–Moody 2-representation. For admissible half-integral or integral cyclotomic parameters, this yields $\mathbb Z$-gradings on the corresponding cyclotomic Brauer algebras at arbitrary level. These results provide a categorical framework toward a Brauer-type analogue of the Brundan–Kleshchev–Ariki theory, involving quantum symmetric pairs and $\imath$-canonical bases. The talk is based on joint work with Mengmeng Gao and Hebing Rui, and, in the integral case, Jun Wu.
报告人简介：
宋林亮，同济大学副教授，主要研究方向为李理论与表示论，主要学术成果发表于Adv. , Math. Z.等国际知名学术期刊，主要工作包括引入了仿射Brauer范畴，仿射web以及仿射Schur范畴，建立了弱三角基理论，为表示论的研究引入了一系列图表范畴的工具和理论。
