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We determine the Clebsch-Gordan and Racah-Wigner coefficients for continuous series of representations of the quantum deformed algebras U_q(sl(2)) and U_q(osp(1|2)). While our results for the former algebra reproduce formulas by Ponsot and Teschner, the expressions for the orthosymplectic algebra are new. Up to some normalization factors, the associated Racah-Wigner coefficients are shown to agree with the fusing matrix in the Neveu-Schwarz sector of N=1 supersymmetric Liouville field theory.
We present a q-difference realization of the quantum superalgebra U_q(sl(M|N)), which includes Grassmann even and odd coordinates and their derivatives. Based on this result we obtain a free boson realization of the quantum affine superalgebra U_q(widehat{sl}(2|1)) of an arbitrary level k.
The periodic $OSp(1|2)$ quantum spin chain has both a graded and a non-graded version. Naively, the Bethe ansatz solution for the non-graded version does not account for the complete spectrum of the transfer matrix, and we propose a simple mechanism
We construct quasilocal conserved charges in the gapless ($|Delta| le 1$) regime of the Heisenberg $XXZ$ spin-$1/2$ chain, using semicyclic irreducible representations of $U_q(mathfrak{sl}_2)$. These representations are characterized by a periodic ac
We offer a complete classification of right coideal subalgebras which contain all group-like elements for the multiparameter version of the quantum group $U_q(mathfrak{sl}_{n+1})$ provided that the main parameter $q$ is not a root of 1. As a conseque
We give a bosonization of the quantum affine superalgebra $U_q(widehat{sl}(N|1))$ for an arbitrary level $k in {bf C}$. The bosonization of level $k in {bf C}$ is completely different from those of level $k=1$. From this bosonization, we induce the W