The Zhang transformation and U_q(osp(1,2l))-Verma modules annihilators

Details The Zhang transformation and U_q(osp(1,2l))-Verma modules annihilators The Zhang transformation and U_q(osp(1,2l))-Verma modules annihilators

1999-11-07

arxiv.org/abs/math/9911041v1

Mathematics

Quantum Algebra

21 pages

Scientific paper

In [ZH], 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-Jimbo and to show how this construction can explain the main theorem of [GL2]: 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 algbra.

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