Orbital Integrals on Reductive Lie Groups & Their Algebras by Francisco Bulnes
Orbital Integrals on Reductive Lie Groups - Table of Contents
PART I: LIE GROUPS & ALGEBRAS THEORY
- 1. Introduction
- 2. Integrals and Special Functions on Lie Groups
- 3. Orbital Integrals on Reductive Lie Groups
- 4. Orbital Integrals on Reductive Lie Algebras
- 5. Integral Transforms on Lie Groups and Algebras
PART II: HARMONIC ANALYSIS & INDUCTION
- 6. Intertwining Operators in Representation Theory
- 7. Representation Theory in Field Theory and Geometry
- 8. Orbital Integrals on Cuspidal Forms
- 9. Applications in Harmonic Analysis
- 10. Cohomological Induction and Generalized G-Modules
APPENDICES: FORMULAS & DIAGRAMS
- A. Integral Formulas on Canonical p-Pairs
- B. Regularity Conditions on a Lie Algebra
- C. Asymptotic Behavior of Matrix Coefficients
- D. Coxeter Diagrams to Integral Transforms
- E. Definition of Real Reductive Groups
What You Will Learn in Orbital Integrals on Reductive Lie Groups
Orbital Integrals on Reductive Lie Groups & Their Algebras by Francisco Bulnes is an authoritative, mathematically rigorous monograph that provides graduate students and specialized researchers with an in-depth treatment of orbital integration techniques across non-commutative harmonic analysis and representation theory. This comprehensive volume guides readers through special functions on Lie algebras, orbital integrals on real reductive groups, intertwining operators, representation theory applications in field theory, cuspidal forms, cohomological induction, and infinite-dimensional G-modules with exceptional analytical precision.
Designed for graduate mathematicians, theoretical physicists, differential geometers, and representation theory researchers, this advanced text bridges pure differential geometry and modern mathematical physics. Bulnes details step-by-step mathematical formulations for integral transforms on Lie groups, matrix coefficient asymptotics, canonical p-pairs, Coxeter diagram applications, and regularity conditions on Lie algebras. Whether you are analyzing trace formulas, studying quantum field theory symmetries, or investigating generalized orbit methods, this book offers an indispensable roadmap.
Recognized globally for its deep synthesis of integral geometry and continuous symmetry groups, it stands as one of the best advanced books on orbital integrals and Lie algebra harmonic analysis. By connecting geometric orbits directly to infinite-dimensional representations, it serves as an essential tool for mastering orbital integration and Lie group analysis with confidence.
Book Details & Specifications
Title:
Orbital Integrals on Reductive Lie Groups & Their Algebras by Francisco Bulnes
Publisher:
InTech
Year:
2013
Pages:
181
Type:
PDF
Language:
English
ISBN-10 #:
ISBN-13 #:
978-953-51-1007-1
License:
CC BY 3.0
Amazon:
Amazon
About the Author: Dr. Francisco Bulnes
The author Dr. Francisco Bulnes
is a Mexican mathematician and physicist, currently serving as the Director of the International Advanced Research in Mathematics and Engineering (IINAMEI) and the Research Department at the Technological Institute of Higher Studies of Chalco (TESCHA). He earned his Ph.D. in Mathematical Sciences from the National Autonomous University of Mexico (UNAM) and has completed postdoctoral research in Cuba and Russia. Dr. Bulnes has authored over 150 research papers and several books, with his work gaining international recognition, particularly in Eastern Europe, the Middle East, and Asia. His research interests encompass algebraic geometry, mathematical physics, infinite Lie theory, global analysis, and various aspects of theoretical physics, including quantum field theory (QFT), quantum electrodynamics (QED), and topological field theory (TFT). He has received numerous honors, including honorary doctorates and awards from universities and organizations worldwide.
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