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

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