Double-bosonization and Majid's conjecture(IV): Type-crossings from A to BCD

作     者：HU HongMei HU NaiHong 

作者机构：Department of Mathematics SKLPMMP East China Normal University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2016年第59卷第6期

页      面：1061-1080页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11271131) 

主　　题：double-bosonization braided category braided groups type-crossing construction normalizedR-matrix representations 

摘      要：Both in Majid s double-bosonization theory and in Rosso s quantum shuffle theory, the rankinductive and type-crossing construction for U_q(g) s is still a remaining open question. In this paper, working in Majid s framework, based on the generalized double-bosonization theorem we proved before, we further describe explicitly the type-crossing construction of U_q(g) s for(BCD)_n series directly from type An-1via adding a pair of dual braided groups determined by a pair of(R, R′)-matrices of type A derived from the respective suitably chosen representations. Combining with our results of the first three papers of this series, this solves Majid s conjecture, i.e., any quantum group U_q(g) associated to a simple Lie algebra g can be grown out of U_q(sl_2)recursively by a series of suitably chosen double-bosonization procedures.