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Dirac Operators in Representation Theory (Mathematics: Theory & Applications) by Jing-Song Huang; Pavle Pandžić is a nonfiction available to read on EtoBox.

What is Dirac Operators in Representation Theory (Mathematics: Theory & Applications) about?

This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Dirac operators are widely used in physics, differential geometry, and group-theoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined using Dirac operators, is a far-reaching generalization that connects index theory in differential geometry to representation theory. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. Key topics covered include: \* Proof of Vogan's conjecture on Dirac cohomology \* Simple proofs of many classical theorems, such as the Bott–Borel–Weil theorem and the Atiyah–Schmid theorem \* Dirac cohomology, defined by Kostant's cubic Dirac operator, along with other closely related kinds of cohomology, such as n-cohomology and (g,K)-cohomology \* Cohomological parabolic induction and $A\_q(\lambda)$ modules \* Discrete series theory, characters, existence and exhaustion \* Sharpening of the Langlands formula on multiplicity of aut

Who reads Dirac Operators in Representation Theory (Mathematics: Theory & Applications)?

Author

Jing-Song Huang; Pavle Pandžić

Publisher

Birkhäuser Boston : Imprint: Birkhäuser

Published

2007

Language

EN

ISBN

9786610865901

Category

nonfiction

Subjects

Mathematics, Science, Physics