Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 by Vladimir Dobrev

Author:Vladimir Dobrev
Language: eng
Format: epub
ISBN: 9789811327155
Publisher: Springer Singapore

Both and DIM algebras have the structure of a quasi-triangular Hopf algebra with the Drinfeld coproduct , that makes them suitable for the definition of qIS. However, the DIM algebra exhibits an extra feature: in addition to , it has a second central element given by . Correspondingly, two grading elements can be introduced, and the universal -matrix depends on two spectral parameters. Here, we consider only representations with integer levels . More precisely, our construction involves vertical representations, of levels (0, m), and horizontal representations of levels (1, n).

Horizontal representations act on the physical space of the qIS. They are the equivalent of the level one representations for [18]. These Fock representations are defined upon the modes of a free boson satisfying

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