Virtual characters and constant coefficient invariant eigendistributions on a semisimple Lie group
Let G be a connected semisimple acceptable Lie group with finite center. An invariant Eigendistribution on G is a distribution which is invariant under all inner automorphisms of G and a simultaneous Eigendistribution of two-sided invariant differential operators on G. By a result of Harish-Chandra one can assign to every irreducible representation an invariant Eigendistribution, its character. The author proves that the space of invariant Eigendistributions with constant coefficients is spanned by the characters of irreducible representations.
connected semisimple acceptable Lie group
scientific article; zbMATH DE number 3946488