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.
No keywords uploaded!
[ Download ] [ 2019-09-23 15:33:58 uploaded by Ivanip ] [ 11 downloads ] [ 0 comments ]
@inproceedings{ivan2012positive,
  title={Positive Representations of Split Real Simply-laced Quantum Groups},
  author={Ivan Chi-Ho Ip},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190923153358283283509},
  booktitle={Preprint},
  year={2012},
}
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.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved