Presents explicit representations of Lie algebras

Addresses interactions with partial differential equations

Examines associated new hypergeometric functions with root systems and quantum many-body systems in one dimension

Connects Lie algebras with coding theory

Autorentext
In 1992, Xiaoping Xu obtained his Ph.D. from Rutgers University in United States. He had worked at the Hong Kong University of Sciences and Technology from 1992 to 2002. He has been a professor at Institute of Mathematics of Chinese Academy of Sciences since 2002 and a professor at the University at Chinese Academy of Sciences since 2014.

Klappentext

Presents explicit representations of Lie algebras Addresses interactions with partial differential equations Examines associated new hypergeometric functions with root systems and quantum many-body systems in one dimension Connects Lie algebras with coding theory

Zusammenfassung

Presents explicit representations of Lie algebras

Addresses interactions with partial differential equations

Examines associated new hypergeometric functions with root systems and quantum many-body systems in one dimension

Connects Lie algebras with coding theory

Inhalt
Preface.- Introduction.- I Fundament of Lie Algebras.- Preliminary of Lie Algebras.- Semisimple Lie Algebras.- Root Systems.- Isomorphisms, Conjugacy and Exceptional Types.- Highest-Weight Representation Theory.- II Explicit Representations.- Representations of Special Linear Algebras.- Representations of Even Orthogonal Lie Algebras.- Representations of Odd Orthogonal Lie Algebras.- Representations of Symplectic Lie Algebras.- Representations of G 2 and F 4.- Representations of E6.- Representations of E.- III Related Topics.- Oscillator Representations of gl(n | m) and osp(n | 2m).- Representation Theoretic Codes.- Path Hypergeometric Functions.- Bibliography.- Index.