Weyl's Character Formula for Finite Dimensional Semisimple Lie Algebras

Panja, Saikat (2017) Weyl's Character Formula for Finite Dimensional Semisimple Lie Algebras. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Saikat Panja (14IP017)) Dissertation_14IP017.pdf - Submitted Version Restricted to Repository staff only Download (550kB)

Abstract

We know that every finite dimensional representation V of finite dimensional semisimple Lie algebra L can be decomposed into irreducible representation. Given a maximal toral algebra H of L, we can decompose V as direct sum of weight spaces. Also given a weight λ, there is (upto isomorphism) a unique irreducible representation Vλ of highest weight λ. The problem is to find multiplicities of a particular weight (say μ) in Vλ and finding the dimension of Vλ (if it is finite dimensional). This problem was resolved by Hermann Weyl. We give an exposition of this result in this thesis.

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