Finite dimensionality of irreducible unitary representations of compact quantum groups

Quan, Xiu Chi

doi:10.1090/S0002-9939-1994-1186135-4

Finite dimensionality of irreducible unitary representations of compact quantum groups
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Proc. Amer. Math. Soc. 121 (1994), 851-858 Request permission

Abstract:

In this paper, we study the representations of Hopf ${C^ \ast }$-algebras; the main result is that every irreducible left unitary representation of a Hopf ${C^\ast }$-algebra with a Haar measure is finite dimensional. To prove this result, we first study the comodule structure of the space of Hilbert-Schmidt operators; then we use this comodule structure to show that every irreducible left unitary representation of a Hopf ${C^\ast }$-algebra with a Haar measure is finite dimensional.

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