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Young Tableaux - William Fulton

Young Tableaux

With Applications to Representation Theory and Geometry

(Autor)

Buch | Hardcover
270 Seiten
1997
Cambridge University Press (Verlag)
978-0-521-56144-0 (ISBN)
CHF 78,55 inkl. MwSt
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The author 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 intuitive presentation and numerous exercises make the book suitable for beginning graduate students as well as researchers.
The aim of this book is to develop the combinatorics of Young tableaux and to show 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 these results are used 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 appeared in book form.There are numerous exercises throughout, with hints or answers provided. Researchers in representation theory and algebraic geometry as well as in combinatorics will find Young Tableaux interesting and useful; students will find the intuitive presentation easy to follow.

Part I. Calculus Of Tableux: 1. Bumping and sliding; 2. Words: the plactic monoid; 3. Increasing sequences: proofs of the claims; 4. The Robinson-Schensted-Knuth Correspondence; 5. The Littlewood-Richardson rule; 6. Symmetric polynomials; Part II. Representation Theory: 7. Representations of the symmetric group; 8. Representations of the general linear group; Part III. Geometry: 9. Flag varieties; 10. Schubert varieties and polynomials; Appendix A; Appendix B.

Erscheint lt. Verlag 28.1.1997
Reihe/Serie London Mathematical Society Student Texts
Verlagsort Cambridge
Sprache englisch
Maße 159 x 236 mm
Gewicht 535 g
Themenwelt Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 0-521-56144-2 / 0521561442
ISBN-13 978-0-521-56144-0 / 9780521561440
Zustand Neuware
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