Dirac Operators in Representation Theory
by
Huang, Jing-Song. author.
Title
:
Dirac Operators in Representation Theory
Author
:
Huang, Jing-Song. author.
ISBN
:
9780817644932
Personal Author
:
Huang, Jing-Song. author.
Physical Description
:
XII, 200 p. online resource.
Series
:
Mathematics: Theory & Applications
Contents
:
Lie Groups, Lie Algebras and Representations -- Clifford Algebras and Spinors -- Dirac Operators in the Algebraic Setting -- A Generalized Bott-Borel-Weil Theorem -- Cohomological Induction -- Properties of Cohomologically Induced Modules -- Discrete Series -- Dimensions of Spaces of Automorphic Forms -- Dirac Operators and Nilpotent Lie Algebra Cohomology -- Dirac Cohomology for Lie Superalgebras.
Abstract
:
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 automorphic forms, with applications * Dirac cohomology for Lie superalgebras An excellent contribution to the mathematical literature of representation theory, this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.
Subject Term
:
Mathematics.
Group theory.
Topological Groups.
Operator theory.
Global differential geometry.
Mathematical physics.
Topological Groups, Lie Groups.
Group Theory and Generalizations.
Differential Geometry.
Mathematical Methods in Physics.
Added Author
:
Pandžić, Pavle.
Added Corporate Author
:
SpringerLink (Online service)
Electronic Access
:
Library | Material Type | Item Barcode | Shelf Number | Status |
---|
IYTE Library | E-Book | 506130-1001 | QA252.3 | Online Springer |