Character sheaves on reductive Lie algebras

The paper develops a linearized notion of Lusztig\u27s character sheaves (on Lie algebras rather then on groups), which contains Lusztig\u27s 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)