Superalgebras, their quantum deformations and the induced representation method

Details Superalgebras, their quantum deformations and the induced representation method Superalgebras, their quantum deformations and the induced representation method

1998-10-29

arxiv.org/abs/math/9810170v1

Mathematics

Quantum Algebra

39 pages, LaTex. Work based on preprint IC/96/130 and a talk given at the "V-th National Mathematics Conference", Hanoi, 17-20

Scientific paper

Some introductory concepts and basic definitions of the Lie superalgebras and their quantum deformations are exposed. Especially the induced representation methods in both cases are described. Based on the Kac representation theory we have succeeded in constructing representations of several higher rank superalgebras. When representations of quantum superalgebras are concerned, we have developed a method which can be applied not only to the one-parametric quantum deformations but also to the multi-parametric ones. As an intermediate step the Gel'fand-Zetlin basis description is extended to the case of superalgebras and their quantum deformations. Our approach also allows us to establish in consistent ways defining relations of quantum (super)algebras. Some illustrations are given.

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