摘要: In this talk, we will study the associated varieties and Gelfand-Kirillov dimensions of highest weight (g, K)-modules for noncompact simple Lie groups. In the first part (joint work with Markus Hunziker), we will give a uniform formula to provide the AV and GKdim for all unitary highest weight (g，K)-modules. In the second part (joint work with Xun Xie), by using Lusztig's a-function we will give a combinatoric algorithm for the GKdim of all highest weight modules of simple Lie algebras of type A. In particular, from this algorithm we can easily determine the AV of highest weight (g, K)-modules for the Lie group SU(p,q). Finally, we will give a formula which can determine the AV of highest weight (g, K)-modules for all types. This part is a joint work with Markus Hunziker and Roger Zierau.