  Taking the hypernucleus $^{13}_{~\Lambda}$C as an example, we illustrate the
miscroscopic particle-rotor model for low-lying spectra of hypernuclei. This
approach is based on the beyond-mean-field method, with the particle number and
angular momentum projections. The quantum fluctuation of the mean-field is also
taken into account for the core nucleus using the generator coordinate method.
We show that the impurity effect of $\Lambda$ hyperon, such as a change in
$B(E2)$, is well described with this model. Our calculation indicates that the
most important impurity effect in $sd$-shell hypernuclei is a change in a
deformation parameter rather than in a nuclear size.
