Support varieties of semisimple-character representations for Cartan type Lie algebras

Abstract

In this paper, we study the support varieties for Lie algebras L of Cartan type. We give some description for the support varieties of any finitedimensional L-module with character χ, whenever the height of the character χ is not too large. And a more concrete computation can be made for a class of modules with semisimple characters.