  Recently, topological phases in non-Hermitian systems have attracted much
attention because non-Hermiticity sometimes gives rise to unique phases with no
Hermitian counterparts. Non-Hermitian Bloch Hamiltonians can always be mapped
to doubled Hermitianized Hamiltonians with chiral symmetry, which enables us to
utilize the existing framework for Hermitian systems into the classification of
non-Hermitian topological phases. While this strategy succeeded in the
topological classification of non-Hermitian Bloch Hamiltonians in the presence
of internal symmetries, the generalization of symmetry indicators -- a way to
efficiently diagnose topological phases -- to non-Hermitian systems is still
elusive. In this work, we study a theory of symmetry indicators for
non-Hermitian systems. We define space group symmetries of non-Hermitian Bloch
Hamiltonians as ones of the doubled Hermitianized Hamiltonians. Consequently,
symmetry indicator groups for chiral symmetric Hermitian systems are equivalent
to those for non-Hermitian systems. Based on this equivalence, we list symmetry
indicator groups for non-Hermitian systems in the presence of space group
symmetries. We also discuss the physical implications of symmetry indicators
for some symmetry classes. Furthermore, explicit formulas of symmetry
indicators for spinful electronic systems are included in appendices.
