The local structure of characters

AbstractLet G be a connected real semisimple Lie group with Lie algebra g. Let g = t̆ + s be the Cartan decomposition and K the maximal compact subgroup with Lie algebra t̆. Let Θ be the character of an irreducible representation. Then Θ has an asymptotic expansion at zero (in the sense of Taylor series). As consequences of this expansion we obtain results about the asymptotic directions in which the K-types occur and about the Gelfand-Kirillov dimension of the representation