Young Tableaux: With Applications to Representation Theory and GeometryCambridge University Press, 1997 - 260 Seiten Young tableaux are fillings of the boxes of diagrams that correspond to partitions with positive integers, that are strictly increasing down columns and weakly increasing along rows. 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, the representations of the symmetric and general linear groups, and the geometry of flag varieties. Many of these applications have not been available in book form. |
Inhalt
Calculus of tableaux | 5 |
Words the plactic monoid | 17 |
Increasing sequences proofs of the claims | 30 |
The RobinsonSchenstedKnuth correspondence | 36 |
The LittlewoodRichardson rule | 58 |
Symmetric polynomials | 72 |
Representations of the symmetric group | 83 |
Representations of the general linear group | 104 |
Flag varieties | 131 |
Schubert varieties and polynomials | 154 |
Appendix A Combinatorial variations | 183 |
Keys | 208 |
Answers and references | 226 |
| 248 | |
| 254 | |
Andere Ausgaben - Alle anzeigen
Young Tableaux: With Applications to Representation Theory and Geometry William Fulton Keine Leseprobe verfügbar - 1997 |
Young Tableaux: With Applications to Representation Theory and Geometry William Fulton Keine Leseprobe verfügbar - 1997 |
Häufige Begriffe und Wortgruppen
algebraic algorithm balls basic basis canonical Chern classes coefficient cohomology column bumping conjugate Corollary d₁ defined denote determines dimension direct sum dual elementary elements embedding entries equation example Exercise fact Fl(m flag manifold flag variety follows formula given gives GL(E GLmC Grassmannian homogeneous homomorphism hook length induction integers interchanging intersection irreducible representations isomorphism kernel Knuth equivalent Lemma lexicographic array line bundle linear Littlewood-Richardson Littlewood-Richardson rule matrix module monomial nonnegative nonzero obtained pair P,Q pairs of tableaux partition permutation Proof Proposition prove quotient R-S-K correspondence rectification resp reverse lattice word ring row bumping row-insertion S₁ Schubert polynomials Schubert varieties Schur polynomials shape skew diagram skew tableau slide spanned standard tableau subset subspace subvariety surjection symmetric group symmetric polynomials tableau pair u₁ unique v₁ vector bundle vector space weight vector Young diagram zero σω
Verweise auf dieses Buch
Symmetric Functions, Schubert Polynomials and Degeneracy Loci Laurent Manivel Eingeschränkte Leseprobe - 2001 |