Categorification of Integrable Representations of Quantum Groups  

作　　者：Hao ZHENG 

机构地区：[1]Department of Mathematics, Zhongshan University [2]School of Mathematical Sciences, Peking University

出　　处：《Acta Mathematica Sinica,English Series》2014年第6期899-932,共34页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.10631060 and 11131008)

摘　　要：We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac–Moody algebra. As a byproduct, we obtain a geometric realization of Lusztig＇s canonical bases of these representations as well as a new positivity result. The main ingredient in the underlying geometric construction is a class of micro-local perverse sheaves on quiver varieties.We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac–Moody algebra. As a byproduct, we obtain a geometric realization of Lusztig＇s canonical bases of these representations as well as a new positivity result. The main ingredient in the underlying geometric construction is a class of micro-local perverse sheaves on quiver varieties.

关 键 词：CATEGORIFICATION quantum groups canonical basis 

分 类 号：O152.5[理学—数学] O561.1[理学—基础数学]