Realization Of O(SO_q(2n+1)) Arising From U_q(so(2n+1)) Via Jantzen Approaching

Jantzen gave the defining relations of (?)(SL_q(2)) from the representations of U_q(sl(2)) by the R—matrix (see [10]). The author gives the realization of (?)(SO_q(2n+1)) arising from the (lifting-allowable) representations of U_q(so(2n + 1)) via the Jantzen's approach.The generators and relations of (?){SO_q(2n+1)) are (cf. [1])We can obtain the R-matrix: R= (?)_n o (f|⁾ o P by the natural representation of U_q(so(2n+1)). If we have proved the R_kl^ij in this R-matrix equal to (R|∧)_kl^ij in the defining relations of (?)(SO_q(2n+1)), then we could prove that (?)(SO_q(2n+1)) can be realized by making use of the .R-matrix of the natural representation of U_q(so(2n+1)).In this article, the key is to give the expression of the canonical element The author obtains...