Centers and Representations of the SL(n) quantum Teichmüller Space

Abstract: The SL(n)-skein algebra of a surface can be thought of as a quantization of the surface’s character variety. When n=2, it agrees with the familiar Kauffman bracket skein algebra, so the \mathrm{SL}(n) SL(n)-skein theory can be viewed as a natural generalization. Thanks to the work of Lê and Yu, we know that the SL(n)-skein algebra is closely related to the SL(n) quantum Teichmüller space through the quantum trace map. In this talk, we will look at the centers and representations of both balanced Fock–Goncharov algebras and SL(n)-skein algebras.

mathematical physicsalgebraic geometrygeometric topologyquantum algebra

Audience: researchers in the discipline

Geometry, Algebra and Physics at KIAS