Maximal torus theory for compact quantum groups

Abstract

Associated to any compact quantum group $G\subset U_N^{+}$ is a canonical family of group dual subgroups ${\hat{\Gamma }}_Q\subset G$, parametrized by unitaries $Q\in U_N$, playing the role of "maximal tori" for $G$. We present here a series of conjectures, relating the various algebraic and analytic properties of $G$ to those of the family $\{{\hat{\Gamma }}_Q|Q\in U_N\}$.

arXiv comment18 pages