You can find this in any abstarct harmonic analysis text, eg folland, a course in abstract harmonic analysis prop 2. At the same time, a general theory of harmonic analysis on p adic groups has been built up by harishchandra on the model of lie groups. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus. Dyadic harmonic analysis and the p adic numbers taylor dupuy july, 5, 2011 abstract notes from a talk given in sevilla in 2012. Hecke algebras and harmonic analysis homepages of uvafnwi.
The concepts are liberally illustrated with examples, usually appropriate for an upperlevel graduate student in representation theory or number theory. The stated goal of the conference was to explore recent advances in harmonic analysis on both real and p adic groups. Lpr, density, interchanging limits on r 382 bibliography 391 name index 401 subject index 403. The article also explains how homogeneity enters into waldspurgers analysis of stability for linear combinations of. Some problems in local harmonic analysis university of toronto. If someone nd errors or wants to suggest a reorganization of this material please email me. In this pattern, the fibonacci ratios that give reliable reversals are a. Harmonic analysis on semisimple lie groups, colloquium lectures, university of oregon, a. Introduction the aim of this paper is to give a new proof of the local langlands correspondence for glnover p adic. At the same time, a general theory of harmonic analysis on padic groups has been built. Harmonic analysis is a generalisation of fourier analysis that studies the properties of functions. Gross, cornell university, ithaca, new york, united states expertise.
Silberger introduction to harmonic analysis on reductive p adic groups. The p adic numbers are a counterintuitive arithmetic system that was discovered by the german mathematician kurt hensel in about 1899. It showcases research results in functional analysis. We thus have the homogeneous space gagq which is locally compact and has a gaaction. For example, the characters of the irreducible representations of reductive groups over p adic elds are not yet well understood. Harmonic analysis available for download and read online in other formats. To any such algebraic group we have the pair ga,gq where gq is discrete. Pdf henstockkurzweil type integrals in padic harmonic. Other harmonic patterns extended patterns the crab pattern this is the most precise pattern, which has fixed ratios for the set up. Box 57, 11001 belgrade, yugoslavia 3steklov mathematical institute, russian academy of sciences, moscow, russia.
Constructive quantum field theory, yangmills heat equation, logarithmic sobolev. It concerns quantitative forms of some of the basic theorems of p adic harmonic analysis, such as howes. Pdf multidimensional padic integral in some problems of. Any action of a group on a set gives rise to actions on vector spaces of functions defined on that set. The mathematical sciences research institute msri, founded in 1982, is an independent nonprofit mathematical research institution whose funding sources include the national science foundation, foundations, corporations, and more than 90 universities and institutions.
It is the application of p adic analysis to quantum mechanics. Harmonic analysis overlaps and interacts quite fruitfully with many other. Harmonic analysis on reductive padic groups and lie algebras. In particular, our discussion of the group gf of rational points applies to both real and padic groups. Harmonic analysis on the p adic numbers jordan bell jordan. This paper is based on lectures delivered at the institute for mathematical sciences at the national university of singapore in 2002. The closely related adeles and ideles were introduced in the 1930s by claude chevalley. The institute is located at 17 gauss way, on the university of california, berkeley campus, close to grizzly peak, on the. Introduction to harmonic analysis on reductive padic.
Harmonic analysis is the study of linear actions of groups on vector spaces. Based on lectures by harishchandra at the institute for advanced study, 197173 mathematical notes by allan g. This volume reports these findings and guides the reader towards the latest areas for further research. Lectures on harmonic analysis for reductive adic groups 3 we remark that ostrowskis theorem tells us that the only nondiscrete, locally compact.
Course notes and supplementary material pdf format. Check out this tag for abstract harmonic analysis on abelian locally compact groups, or euclidean harmonic analysis eg, littlewoodpaley theory, singular integrals. Harmonic analysis on reductive padic groups springerlink. Roman bezrukavnikov harmonic analysis on p adic groups and l adic sheaves i will report on a project, partly joint with d. Algorithms, analysis, and applications applied and numerical harmonic analysis 20180122 pdf p adic numbers, p adic analysis, and zetafunctions graduate texts in mathematics. Harmonic analysis and representation theory of padic. P adic quantum mechanics is a relatively recent approach to understanding the nature of fundamental physics.
The institute was held at williams college in williamstown, massachusetts from july 31 to august 18, 1972, and was supported by a grant from the national science foundation. Introduction to padic harmonic analysis james arthur. Introduction to harmonic analysis on reductive p adic groups. Numerous and frequentlyupdated resource results are available from this search. Introduction to harmonic analysis on reductive padic groups. Recall that the local langlands correspondence, which is now a theorem due to harristaylor, 10.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. Group actions, in turn, are important because many mathematical st. Harmonic analysis and representation theory of padic reductive. Varshavsky, which introduces perverse sheaves methods into harmonic analysis on p adic groups. Harmonic analysis on reductive padic groups numdam. A presentation of results in p adic banach spaces, spaces over fields with an infinite rank valuation, frechet and locally convex spaces with schauder bases, function spaces, p adic harmonic analysis, and related areas. The short article of murnaghan contains a summary of some of the basic. One can apply this process of thinking to groups such as gln and rational algebraic groups g.
Many of the supporting proofs have been revised and refined. If g is any group and h a subgroup, we write zghngh for the centralizer normalizer of. Harishchandra has enunciated the cusp form philosophy and proved the plancherel formula that are both tremendously in. The papers in this volume present both expository and research articles on these and related topics, presenting a broad picture of the current state of the art in \p\ adic harmonic analysis. Based on a series of lectures given by harishchandra at the institute for advanced study in 19711973, this book provides an introduction to the theory of harmonic analysis on reductive p adic groups. A conference on harmonic analysis on reductive groups was held at bowdoin college in brunswick, maine from july 31 to august 11, 1989. For instance, the study of decomposing a function on a. Pdf harmonic analysis download full pdf book download.
The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it. James arthur, university of toronto introduction to harmonic analysis on p adic groups tuesday aug 12, 2008 11. Representation theory and harmonic analysis on real and p adic non commutative groups. Lectures on harmonic analysis for reductive adic groups. The notes are as self contained as possible, covering basic number theory and analytic ideas which would probably be familiar to to more advanced readers. Essays in harmonic analysis on padic sl2 geometry of. In particular, important connections between harmonic analysis, wavelet analysis and p adic analysis have been found recently. In order to form a group with respect to addition, the additive identity.
Harmonic analysis on compact abelian groups march 23, 20 is insensitive to leftright issues. This new edition contains a new chapter on p adic and adelic groups, as well as a complementary section on direct and projective limits. Algebraische gruppe analysis groups reductive p adic groups algebra calculus harmonic analysis. Principles of harmonic analysis anton deitmar springer. In this course, we study some basic results in the theory of admissible representations of reductive p adic. This volume contains the proceedings of the ams special session on harmonic analysis and representations of reductive, padic groups. The theory of representation of padic reductive groups has nowadays attained a mature. The cd forms an extreme wave, which would be anywhere from 2. Chapter vi harmonic analysis on p adic groups december 6, 2005 contents 1 representation theory 2 1. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. Partially supported by nserc operating grant a3483. Multidimensional p adic integral in some problems of harmonic analysis article pdf available january 2017 with 56 reads how we measure reads. Mn23 based on lectures by harishchandra at the institute for advanced study, 197173. Historically, this research was inspired by the discovery that the veneziano amplitude of the open bosonic string, which is calculated using an integral over the real numbers, can be generalized to the p adic numbers.