Representations of Semisimple Lie Algebras
نویسنده
چکیده
Let L be a finite-dimensional, semisimple Lie algebra over an algebraically closed field k of characteristic 0. Let H be a fixed Cartan subalgebra of L, and Φ be the root system. Fix a base ∆ = {α1, · · · , αl} of Φ. Let Λ denote the set of dominant, integral linear functions on H. Theorem 0.1. There is a one-to-one correspondence Λ ∼ −→ {isomorphism classes of finite-dimensional irreducible L-modules}. The map associates to each λ ∈ Λ the Verma module V (λ).
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