'This book provides a bridge between two very active and important parts of mathematics and physics, namely the theory of automorphic forms on reductive groups and string theory. The authors have masterfully presented both aspects and their connections, and have provided examples and details at all levels to make the book available to a large readership, including non-experts in both fields. This is a valuable contribution and a welcoming text for graduate students as well.' Freydoon Shahidi, Purdue University, Indiana

'The book is a valuable addition to the literature, and it may inspire more exchange between mathematics and physics at an advanced level.' Anton Deitmar, MathSciNet

'The prerequisites for a profitable reading this book are enormous. Readers without a solid background in algebraic and analytic number theory, classfield theory, modular forms and representation theory will only be able to read a couple of sections. Researchers in these fields will be grateful to the authors and the publisher for providing access to some rather advanced mathematics. The material is presented in a very clear and lucid way; there is an extensive index and a list of references containing 634 items.' Franz Lemmermeyer, zbMATH

This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman–Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.
Les mer
1. Motivation and background; Part I. Automorphic Representations: 2. Preliminaries on p-adic and adelic technology; 3. Basic notions from Lie algebras and Lie groups; 4. Automorphic forms; 5. Automorphic representations and Eisenstein series; 6. Whittaker functions and Fourier coefficients; 7. Fourier coefficients of Eisenstein series on SL(2, A); 8. Langlands constant term formula; 9. Whittaker coefficients of Eisenstein series; 10. Analysing Eisenstein series and small representations; 11. Hecke theory and automorphic L-functions; 12. Theta correspondences; Part II. Applications in String Theory: 13. Elements of string theory; 14. Automorphic scattering amplitudes; 15. Further occurrences of automorphic forms in string theory; Part III. Advanced Topics: 16. Connections to the Langlands program; 17. Whittaker functions, crystals and multiple Dirichlet series; 18. Automorphic forms on non-split real forms; 19. Extension to Kac–Moody groups; Appendix A. SL(2, R) Eisenstein series and Poisson resummation; Appendix B. Laplace operators on G/K and automorphic forms; Appendix C. Structure theory of su(2, 1); Appendix D. Poincaré series and Kloosterman sums; References; Index.
Les mer
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

Produktdetaljer

ISBN
9781107189928
Publisert
2018-07-05
Utgiver
Vendor
Cambridge University Press
Vekt
920 gr
Høyde
235 mm
Bredde
157 mm
Dybde
38 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
584

Om bidragsyterne

Philipp Fleig is a Postdoctoral Researcher at the Max-Planck-Institut für Dynamik und Selbstorganisation, Germany. Henrik P. A. Gustafsson is a Postdoctoral Researcher in the Department of Mathematics at Stanford University, California. Axel Kleinschmidt is a Senior Scientist at the Max-Planck-Institut für Gravitationsphysik, Germany (Albert Einstein Institute) and at the International Solvay Institutes, Brussels. Daniel Persson is an Associate Professor in the Department of Mathematical Sciences at Chalmers University of Technology, Gothenburg.