Differential Operator Approach to■quantum Groups and Their Oscillator Representations

作     者：Zhao Bing FAN Ji Cheng GENG Shao Long HAN Zhao Bing FAN;Ji Cheng GENG;Shao Long HAN

作者机构：College of Mathematical ScienceHarbin Engineering UniversityHarbin 150001P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第5期

页      面：1360-1374页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：partially supported by the NSF of China grant 12271120 the NSF of Heilongjiang Province grant JQ2020A001 the Fundamental Research Funds for the Central Universities。 

主　　题：■quantum group differential operator oscillator representation crystal basis 

摘      要：For a quasi-split Satake diagram,we define a modified q-Weyl algebra,and show that there is an algebra homomorphism between it and the corresponding■quantum group.In other words,we provide a differential operator approach to■quantum groups.Meanwhile,the oscillator representations of■quantum groups are obtained.The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.