This volume higlights progress in the theory regulators and secondary invariants, bringing together concepts, methods, results from analysis, differential geometry, algebraic geometry and number theory. A historical and mathematical overview of the theory of regulators is presented followed by articles written and refereed by experts in their respective fields.
This volume higlights progress in the theory regulators and secondary invariants, bringing together concepts, methods, results from analysis, differen...
A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis...
A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted...
This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. Developments in integrable models reveal an unexpected link between representation theory and statistical mechanics through combinatorics. For example, Young tableaux, which describe the basis of irreducible representations, appear in the Bethe Ansatz method in quantum spin chains as labels for the eigenstates of Hamiltonians. this text presents results and ideas from three viewpoints: representation theory; integrable models; and combinatorics.
This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. Developments in integrab...
Systematically develops the theory of Frobenius splittings and covers all its major developments.
Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings--definitions, properties and examples--to cutting edge research.
Systematically develops the theory of Frobenius splittings and covers all its major developments.
The volume is dedicated to AA. Kirillov and emerged from an international con- ference which was held in Luminy, Marseille, in December 2000, on the occasion 6 of Alexandre Alexandrovitch's 2 th birthday. The conference was devoted to the orbit method in representation theory, an important subject that influenced the de- velopment of mathematics in the second half of the XXth century. Among the famous names related to this branch of mathematics, the name of AA Kirillov certainly holds a distinguished place, as the inventor and founder of the orbit method. The research articles in this volume...
The volume is dedicated to AA. Kirillov and emerged from an international con- ference which was held in Luminy, Marseille, in December 2000, on the o...
From reviews of the first edition: "The important feature of the present book is that it starts from the beginning (with only a very modest knowledge assumed) and covers all important topics... The book is very carefully organized and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of fundamentals of the theory will certainly be a basic reference and text book in the future." -- Newsletter of the EMS "This is a fundamental book and none, beginner or expert, could afford to ignore it. Some results are really difficult to be found in other...
From reviews of the first edition: "The important feature of the present book is that it starts from the beginning (with only a very modest knowledge ...
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g = j] cannot both be very small." ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark....
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was hi...
Contains new results on different aspects of Lie theory, including Lie superalgebras, quantum groups, crystal bases, representations of reductive groups in finite characteristic, and the geometric Langlands program
Contains new results on different aspects of Lie theory, including Lie superalgebras, quantum groups, crystal bases, representations of reductive g...
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter...
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of t...
