Dimension formulas of the highest weight exceptional Lie algebra-modules

Abstract

Given a complex simple exceptional Lie algebra $ \mathfrak g $, let $ \mathscr V_\lambda $ be an irreducible finite-dimensional $ \mathfrak g $-module with highest weight $ \lambda $. We provide the precise dimension formula of $ \dim \mathscr V_{\lambda} $.

Keywords

• dynkin index
• weyl dimension formula
• exceptional lie algebra
• highest weight module
• symbolic computation