Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

Streszczenie

We ask whether for a given unitary representation $U$ of a compact quantum group $\mathbb G$ the associated operator $\rho_{U}\in\operatorname{Mor}(U,U^{\scriptscriptstyle\rm cc})$ has spectrum invariant under inversion; we then say that $\rho_{U}$ has symmetric eigenvalues. This is not always the case. However, we give an affirmative answer whenever a certain condition on the growth of the dimensions of irreducible subrepresentations of tensor powers of $U$ is imposed. This condition is satisfied whenever $\widehat{\mathbb G}$ is of subexponential growth.