Highest-Weight Representation Theory

Xiaoping Xu ()
Additional contact information
Xiaoping Xu: Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Institute of Mathematics

Chapter Chapter 5 in Representations of Lie Algebras and Partial Differential Equations, 2017, pp 125-151 from Springer

Abstract: Abstract We study finite-dimensional irreducible representations of a finite-dimensional semisimple Lie algebra over $$\mathbb {C}$$ C . First we introduce the universal enveloping algebra of a Lie algebra and prove the Poincaré-Birkhoff-Witt (PBW) Theorem. Then we use the universal enveloping algebra o to construct Verma modules. Moreover, we prove that any finite-dimensional-module is the quotient of a Verma module modulo its maximal proper submodule, whose generators are explicitly given. Furthermore, the Weyl’s character formula is derived and the dimensional formula is determined.

Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-6391-6_5

Ordering information: This item can be ordered from
http://www.springer.com/9789811063916

DOI: 10.1007/978-981-10-6391-6_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().