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THE CLASSICAL LIMIT OF REPRESENTATION THEORY OF THE QUANTUM PLANE

IVAN C. H. IP

Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba 277-8583, Japan

https://doi.org/10.1142/S0129167X13500316Cited by:1 (Source: Crossref)

Abstract

We showed that there is a complete analogue of a representation of the quantum plane where |q| = 1, with the classical ax+b group. We showed that the Fourier transform of the representation of on has a limit (in the dual corepresentation) toward the Mellin transform of the unitary representation of the ax+b group, and furthermore the intertwiners of the tensor products representation has a limit toward 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 corepresentation that is dual to the representation of above, and also correspond precisely to the classical family of unitary representation of the ax+b group.

Keywords:

AMSC: 20G42, 81R50

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