  The classical uncertainty principles deal with functions on abelian groups.
In this paper, we discuss the uncertainty principles for finite index
subfactors which include the cases for finite groups and finite dimensional Kac
algebras. We prove the Hausdorff-Young inequality, Young's inequality, the
Hirschman-Beckner uncertainty principle, the Donoho-Stark uncertainty
principle. We characterize the minimizers of the uncertainty principles. We
also prove that the minimizer is uniquely determined by the supports of itself
and its Fourier transform. The proofs take the advantage of the analytic and
the categorial perspectives of subfactor planar algebras. Our method to prove
the uncertainty principles also works for more general cases, such as Popa's
$\lambda$-lattices, modular tensor categories etc.
