Positive Representations of Split Real Simply-Laced Quantum Groups

  • Ivan C. H. Ip

    Hong Kong University of Science and Technology, Hong Kong
Positive Representations of Split Real Simply-Laced Quantum Groups cover

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Abstract

We construct the positive principal series representations for where is of simply-laced type, parametrized by where is the rank of . We describe explicitly the actions of the generators in the positive representations as positive essentially self-adjoint operators on a Hilbert space, and prove the transcendental relations between the generators of the modular double. We define the modified quantum group of the modular double and show that the representations of both parts of the modular double commute weakly with each other, there is an embedding into a quantum torus algebra, and the commutant contains its Langlands dual.

Cite this article

Ivan C. H. Ip, Positive Representations of Split Real Simply-Laced Quantum Groups. Publ. Res. Inst. Math. Sci. 56 (2020), no. 3, pp. 603–646

DOI 10.4171/PRIMS/56-3-6