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William Fulton, Flags, Schubert polynomials, degeneracy loci, and determinantal formulas, Duke Math. J. 65 (1992), no. 3, 381–420.
S. B. Mulay, Determinantal loci and the flag variety, Adv. Math. 74 (1989), no. 1, 1–30.
Jürgen Herzog and Ngô Viêt Trung, Gröbner bases and multiplicity of determinantal and Pfaffian ideals, Adv. Math. 96 (1992), no. 1, 1–37.
Aldo Conca, Ladder determinantal rings, J. Pure Appl. Algebra 98 (1995), no. 2, 119–134.
J. V. Motwani and M. A. Sohoni, Divisor class groups of ladder determinantal varieties, J. Algebra 186 (1996), no. 2, 338–367.
Aldo Conca and Jürgen Herzog, Ladder determinantal rings have rational singularities, Adv. Math. 132 (1997), no. 1, 120–147.
N. Gonciulea and V. Lakshmibai, Schubert varieties, toric varieties, and ladder determinantal varieties, Ann. Inst. Fourier (Grenoble) 47 (1997), no. 4, 1013–1064.
C. Krattenthaler and M. Prohaska, A remarkable formula for counting nonintersecting lattice paths in a ladder with respect to turns, Trans. Amer. Math. Soc. 351 (1999), no. 3, 1015–1042.
Sara Billey and V. Lakshmibai, Singular loci of Schubert varieties, Birkhäuser, Boston, MA, 2000.
N. Gonciulea and V. Lakshmibai, Singular loci of ladder determinantal varieties and Schubert varieties, J. Algebra 229 (2000), no. 2, 463–497.
Nicolae Gonciulea and Claudia Miller, Mixed ladder determinantal varieties, J. Algebra 231 (2000), no. 1, 104–137.
James E. Humphreys, Reflection groups and Coxeter groups, Cambridge University Press, Cambridge, 1990.
Anders Björner and Francesco Brenti, Combinatorics of Coxeter groups, Graduate Texts in Mathematics, Springer-Verlag, 2004, to appear.
Alain Lascoux and Marcel-Paul Schützenberger, Polynômes de Schubert, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 13, 447–450.
I. N. Bernšteĭn, I. M. Gelfand, and S. I. Gelfand, Schubert cells, and the cohomology of the spaces G/P, Usp. Mat. Nauk 28 (1973), no. 3 (171), 3–26.
Michel Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup. (4) 7 (1974), 53–88.
Laurent Manivel, Symmetric functions, Schubert polynomials and degeneracy loci, SMF/AMS Texts and Monographs Vol. 6, American Mathematical Society, Providence, RI, 2001, translated from the 1998 French original by John R. Swallow, Cours Spécialisés [Specialized Courses], 3.
Ian G. Macdonald, Notes on Schubert polynomials, Publications du LACIM, Universitè du Québec à Montréal, Montréal, 1991.
William Fulton and Piotr Pragacz, Schubert varieties and degeneracy loci, Springer-Verlag, Berlin, 1998.
Allen Knutson and Ezra Miller, Gröbner geometry of Schubert polynomials, Ann. Math. (2), to appear, 2004. arXiv:math.AG/0110058 Theorem A
Burt Totaro, The Chow ring of a classifying space, Algebraic K-theory (Seattle, WA, 1997), American Mathematical Society, Providence, RI, 1999, pp. 249–281.
Dan Edidin and William Graham, Equivariant intersection theory, Invent. Math. 131 (1998), no. 3, 595–634.
Alain Lascoux and Marcel-Paul Schützenberger, Structure de Hopf de l’anneau de cohomologie et de l’anneau de Grothendieck d’une variété de drapeaux, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), no. 11, 629–633.
Allen Knutson and Ezra Miller, Gröbner geometry of Schubert polynomials, Ann. Math. (2), to appear, 2004. arXiv:math.AG/0110058
Anders Skovsted Buch, Grothendieck classes of quiver varieties, Duke Math. J. 115 (2002), no. 1, 75–103. Theorem 2.1
G. Z. Giambelli, Ordine di una varietà più ampia di quella rappresentata coll’annullare tutti i minori di dato ordine estratti da una data matrice generica di forme, Mem. R. Ist. Lombardo 3 (1904), no. 11, 101–135.
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(2005). Matrix Schubert varieties. In: Combinatorial Commutative Algebra. Graduate Texts in Mathematics, vol 227. Springer, New York, NY. https://doi.org/10.1007/0-387-27103-1_15
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