Character sheaves on reductive Lie algebras

The paper develops a linearized notion of Lusztig's character sheaves (on Lie algebras rather then on groups), which contains Lusztig's class of character sheaves on Lie algebras. The theory is independent of the characteristic $p$ of the field, and we use it to provide elementary proofs of some results of Lusztig (for instance, the observation that on groups all cuspidal sheaves are character sheaves).