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arXiv · 1803.05658

Symmetry of eigenvalues of operators associated with representations of compact quantum groups

Jacek Krajczok
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Abstract

We ask the question whether for a given unitary representation $U$ the associated operator $\rho_{U}\in\operatorname{Mor}(U,U^{c\, c})$ has spectrum invariant under inversion -- in this case we say that $\rho_{U}$ has symmetric eigenvalues. This does not have to be the case. However, we give affirmative answer whenever a certain condition on the growth of dimensions of irreducible subrepresentations of tensor powers of $U$ is imposed. This condition is satisfied whenever $\widehat{\mathbb{G}}$ is of subexponential growth.

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Jacek Krajczok. 2018-03-15. Symmetry of eigenvalues of operators associated with representations of compact quantum groups. https://arxiv.org/abs/1803.05658

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