Quantum SL(2,R) and its irreducible representations

Date/heure
7 avril 2022
14:15

Lieu
Salle de séminaires Metz

Oratrice ou orateur
Joel Right Dzokou Talla (Vrije Universiteit Brussel)

Catégorie d'évènement
Séminaire Théorie de Lie, Géométrie et Analyse


Résumé

Let I and J be two orthogonal respectively left and right coideal $*$-subalgebras of a dual pair of Hopf $*$-algebras. We define the Drinfeld double coideal of J and I. Next, we define for $0<q<1$ the unital $*$-algebra $U_q(sl(2,R))$, quantizing the universal enveloping $*$-algebra of $sl(2, R)$, as the Drinfeld double of the equatorial Podles sphere coideal $*$-subalgebra of $O_q(SU(2))$ and its associated orthogonal coideal $*$-subalgebra of $U_q(su(2))$. We finally classify its admissible irreducible $*$-representations.