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- WILLIAM FULTON
- 1998

This is a closed subscheme ofX ; locally, where the bundles are trivial, this is defined by vanishing of the minors of size rij +1 in the product of matrices giving the map φj ◦ · · · ◦ φi+1 from Ei to Ej , for all i < j. Not all rank conditions give reasonable loci. Those that do—and the only ones we will consider—are characterized by the conditions rij ≤… (More)

- WILLIAM FULTON
- 2000

We describe recent work of Klyachko, Totaro, Knutson, and Tao, that characterizes eigenvalues of sums of Hermitian matrices, and decomposition of tensor products of representations of GLn(C). We explain related applications to invariant factors of products of matrices, intersections in Grassmann varieties, and singular values of sums and products of… (More)

- WILLIAM FULTON
- 1997

The aim of this paper is to introduce some polynomials that specialize to all previously known Schubert polynomials: the classical Schubert polynomials of Lascoux and Schützenberger [L-S], [M], the quantum Schubert polynomials of Fomin, Gelfand, and Postnikov [F-G-P], and quantum Schubert polynomials for partial flag varieties of Ciocan-Fontanine [CF2].… (More)

- W. FULTON
- 2008

We give a formula for the smallest powers of the quantum parameters q that occur in a product of Schubert classes in the (small) quantum cohomology of general flag varieties G/P . We also include a complete proof of Peterson’s quantum version of Chevalley’s formula, also for general G/P ’s.

- DETERMINANTAL FORMULAS, WILLIAM FULTON

Under appropriate conditions on the rank function r, which guarantee that, for generic h, f,(h) is irreducible, we prove a formula for the class [f,(h)] of this locus in the Chow or cohomology ring of X, as a polynomial in the Chern classes of the vector bundles. When expressed in terms of Chern roots, these polynomials are the "double Schubert polynomials"… (More)

- William Fulton
- Advanced book classics
- 1989

- WILLIAM FULTON
- 2008

Answering a question raised by S. Friedland, we show that the possible eigenvalues of Hermitian matrices (or compact operators) A, B, and C with C ≤ A+B are given by the same inequalities as in Klyachko’s theorem for the case where C = A + B, except that the equality corresponding to tr(C) = tr(A) + tr(B) is replaced by the inequality corresponding to tr(C)… (More)

- Marlon G Boarnet, Kenneth Joh, Walter Siembab, William Fulton, Mai Thi Nguyen
- Urban studies
- 2011

This paper reports results from a detailed travel diary survey of 2125 residents in the South Bay area of Los Angeles County - a mature, auto-oriented suburban region. Study areas were divided into four centres, typical of compact development or smart growth, and four linear, auto-oriented corridors. Results show substantial variation in the amount of… (More)

The purpose of this exposition is to give a simple treatment of Knutson and Tao’s recent proof of the saturation conjecture [10]. A finite dimensional irreducible polynomial representation of GLn(C) is determined by its highest weight, which is a weakly decreasing sequence of n non-negative integers, also called a partition [5, §8]. The irreducible… (More)