Books by William Fulton
Young Tableaux: With Applications to Representation Theory and Geometry (London Mathematical Society Student Texts, Series Number 35)
This book develops the combinatorics of Young tableaux and shows them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties. The first part of the book is a self-contained presentation of the basic combinatorics of Young tableaux, including the remarkable constructions of "bumping" and "sliding", and several interesting correspondences. In Part II the author uses these results to study representations with geometry on Grassmannians and flag manifolds, including their Schubert subvarieties, and the related Schubert polynomials. Much of this material has never before appeared in book form. There are numerous exercises throughout, with hints and answers provided. Researchers in representation theory and algebraic geometry as well as in combinatorics will find this book interesting and useful, while students will find the intuitive presentation easy to follow.
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Representation Theory: A First Course (Graduate Texts in Mathematics, 129)
The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.
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Algebraic Topology: A First Course (Graduate Texts in Mathematics, 153)
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups
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Camp Lo's Uptown Saturday Night (33 1/3)
by William Fulton, Patrick Rivers
Geechi Suede and Sonny Cheeba are Camp Lo. These two emcees from the Bronx, NY entered the American hip hop scene with an insider slang that bewildered listeners as they radiated the look of a bygone era of black culture. In 1996, they collaborated with producer Ski and a host of other contributors to create Uptown Saturday Night, featuring the seminal single “Luchini (a.k.a. This is It).” While other 1990s rappers referred to 1970s Blaxploitation culture, Camp Lo were self-described “time travelers” who weaved the slang and style of a soulful past into state-of-the-art lyrical flows.
Uptown Saturday Night is a tapestry of 1970s black popular culture and 1990s New York City hip hop. This volume will detail how the album's fantastic world of “Coolie High” reflected classic films like Cooley High and the Sidney Poitier film from which the album's title is derived, and promoted vintage slang and fashion. The book features new interviews with Camp Lo, producer Ski, Trugoy the Dove from De La Soul, Ish from Digable Planets, and others, and offers musical and cultural analyses that detail the development of the album and its essential contributions to a post-soul aesthetic.
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