Positive Representations of Split Real Simply-laced Quantum Groups

Ivan Chi-Ho Ip HKUST

TBD mathscidoc:1909.43018

Preprint, 2012
We construct the positive principal series representations for Uq(gR) where g is of simply-laced type, parametrized by Rr where r is the rank of g. In particular, the positivity of the operators and the transcendental relations between the generators of the modular double are shown. We define the modified quantum group $\mathbf{U}_{q\tilde{q}(g_R)$ of the modular double and show that the representation of both parts of the modular double commute with each other, there is an embedding into the q-tori polynomials, and the commutant is the Langlands dual. We write down explicitly the action for type An,Dn and give the details of calculations for type E6,E7 and E8.
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  title={Positive Representations of Split Real Simply-laced Quantum Groups},
  author={Ivan Chi-Ho Ip},
Ivan Chi-Ho Ip. Positive Representations of Split Real Simply-laced Quantum Groups. 2012. In Preprint. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190923153358283283509.
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