Positive Representations of Split Real Simply-laced Quantum Groups

Details Positive Representations of Split Real Simply-laced Quantum Groups Positive Representations of Split Real Simply-laced Quantum Groups

2012-03-09

arxiv.org/abs/1203.2018v3

Mathematics

Representation Theory

Dedicated to Igor Frenkel on his 60th birthday. Added Section 11 which proved Conjecture 1.5 (now Theorem 11.1) from previous

Scientific paper

We construct the positive principal series representations for $U_q(g_R)$ where $g$ is of simply-laced type, parametrized by $R^r$ 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 $A_n, D_n$ and give the details of calculations for type $E_6,E_7$ and $E_8$.

Affiliated with

Also associated with

No associations

Rating

Positive Representations of Split Real Simply-laced Quantum Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive Representations of Split Real Simply-laced Quantum Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive Representations of Split Real Simply-laced Quantum Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-302010