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...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.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11271131)
文摘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.
