The Universal $C^{\ast }$-Algebra of the Quantum Matrix Ball and its Irreducible $\ast$-Representations

Abstract

We prove that any irreducible $\ast$-representation of $\mathrm{Pol}({\mathrm{Mat}}_n{)}_q$ can be 'lifted' to an irreducible *-representation of $\mathbb{C}[S{U}_{2n}{]}_q$, this result is then used to show the existence of the universal enveloping $C^{\ast }$- algebra of $\mathrm{Pol}({\mathrm{Mat}}_n{)}_q$ and to prove that it is isomorphic to the closure of the image of the Fock representation. Moreover, we also classify all irreducible $\ast$-representations of $\mathrm{Pol}({\mathrm{Mat}}_n{)}_q$ using a diagram approach.

References in corpus (1)

• Quantum matrix ball: the Cauchi-Szegö kernel and the Shilov boundary

Cited by in corpus (1)

• On $q$-tensor product of Cuntz algebras