Searches for sterile neutrinos with IceCube DeepCore

We show that study of the atmospheric neutrinos in the 10--100 GeV energy range by DeepCore sub-array of the IceCube Neutrino Observatory can substantially constrain the mixing of sterile neutrinos of mass $\sim 1$ eV with active neutrinos. In the scheme with one sterile neutrino we calculate $\nu_\mu-$ and $\bar{\nu}_\mu-$ oscillation probabilities as well as zenith angle distributions of $\nu_\mu^{CC}$ events in different energy intervals in DeepCore. The distributions depend on the mass hierarchy of active neutrinos. Therefore, in principle, the hierarchy can be identified, if $\nu_s$ exists. After a few years of exposure the DeepCore data will allow to exclude the mixing $|U_{\mu 4}|^2 \geq 0.02$ indicated by the LSND/MiniBooNE results. Combination of the DeepCore and high energy IceCube data will further improve sensitivity to $\nu_s$ mixing parameters.