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arXiv · 1012.4145

The Classical Limit of Representation Theory of the Quantum Plane

Ivan Chi-Ho Ip
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Abstract

We showed that there is a complete analogue of a representation of the quantum plane B_q where |q|=1, with the classical ax+b group. We showed that the Fourier Transform of the representation of B_q on H=L^2(R) has a limit (in the dual co-representation) towards the Mellin transform of the unitary representation of the ax+b group, and furthermore the intertwiners of the tensor products representation has a limit towards the intertwiners of the Mellin transform of the classical ax+b representation. We also wrote explicitly the multiplicative unitary defining the quantum ax+b semigroup and showed that it defines the co-representation that is dual to the representation of B_q above, and also correspond precisely to the classical family of unitary representation of the ax+b group.

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Ivan Chi-Ho Ip. 2012-09-18. The Classical Limit of Representation Theory of the Quantum Plane. https://arxiv.org/abs/1012.4145

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