Representations of Lie Algebras and Partial Differential Equations

• Main Author: Xu, Xiaoping (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2017.
• Subjects: Mathematics.; Algebra.; Partial differential equations.; Special functions.; Algorithms.; Partial Differential Equations.; Special Functions.

This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students.  Further, it presents...

Table of Contents:

• 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. .