Abstract
Abstract
We study irreducible spherical unitary representations of the Drinfeld double of the q-deformation of a connected simply connected compact Lie group,
which can be considered as a quantum analogue of the complexification of the Lie group.
In the case of
\mathrm{SU}_{q}(3)
, we give a complete classification of such representations.
As an application, we show the Drinfeld double of the quantum group
\mathrm{SU}_{q}(2n+1)
has property (T), which also implies central property (T) of the dual of
\mathrm{SU}_{q}(2n+1)
.
Funder
Japan Society for the Promotion of Science
Program for Leading Graduate Schools, MEXT, Japan
Subject
Applied Mathematics,General Mathematics
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