Abstract
R. B. Zhang found a way to link certain formal deformations of the Lie algebra o(2l+1) and the Lie superalgebra osp(1,2l). The aim of this article is to reformulate the Zhang transformation in the context of the quantum enveloping algebras a la Drinfeld and Jimbo and to show how this construction can explain the main theorem of Gorelik and Lanzmann: the annihilator of a Verma module over the Lie superalgebra osp(1,2l) is generated by its intersection with the centralizer of the even part of the enveloping algebra.
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