Schubert polynomials and quiver formulas
作者： Alexander Yong , Harry Tamvakis , Andrew Kresch , Anders S. Buch
DOI: 10.1215/S0012-7094-04-12214-6
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摘要: Fulton's universal Schubert polynomials [F3] represent degeneracy loci for morphisms of vector bundles with rank conditions coming from a permutation. The quiver formula of Buch and Fulton [BF] expresses these as an integer linear combination products Schur determinants. We present positive, nonrecursive combinatorial the coefficients. Our result is applied to obtain new expansions for the Lascoux Schutzenberger [LS1] and explicit Giambelli formulas in the classical quantum cohomology ring any partial flag variety.
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sci-hub.se 参考文章(18)
Sara C. Billey, William Jockusch, Richard P. Stanley, Some Combinatorial Properties of Schubert Polynomials Journal of Algebraic Combinatorics. ,vol. 2, pp. 345- 374 ,(1993) , 10.1023/A:1022419800503
William Fulton, Flags, Schubert polynomials, degeneracy loci, and determinantal formulas Duke Mathematical Journal. ,vol. 65, pp. 381- 420 ,(1992) , 10.1215/S0012-7094-92-06516-1
Frank Sottile, Nantel Bergeron, Schubert polynomials, the Bruhat order, and the geometry of flag manifolds Duke Mathematical Journal. ,vol. 95, pp. 373- 423 ,(1998) , 10.1215/S0012-7094-98-09511-4
Ian Grant Macdonald, Notes on Schubert polynomials LACIM, Université du Québec à Montréal. ,(1991)
Sergey Fomin, Sergei Gelfand, Alexander Postnikov, Quantum Schubert polynomials Journal of the American Mathematical Society. ,vol. 10, pp. 565- 596 ,(1997) , 10.1090/S0894-0347-97-00237-3
Ionu? Ciocan-Fontanine, On quantum cohomology rings of partial flag varieties Duke Mathematical Journal. ,vol. 98, pp. 485- 524 ,(1999) , 10.1215/S0012-7094-99-09815-0
Sergey Fomin, Curtis Greene, Noncommutative Schur functions and their applications Discrete Mathematics. ,vol. 306, pp. 1080- 1096 ,(2006) , 10.1016/J.DISC.2006.03.028
William Fulton, Universal Schubert polynomials Duke Mathematical Journal. ,vol. 96, pp. 575- 594 ,(1999) , 10.1215/S0012-7094-99-09618-7
Richard P. Stanley, On the Number of Reduced Decompositions of Elements of Coxeter Groups European Journal of Combinatorics. ,vol. 5, pp. 359- 372 ,(1984) , 10.1016/S0195-6698(84)80039-6
A. N. Kirillov, Cauchy Identities for Universal Schubert Polynomials Journal of Mathematical Sciences. ,vol. 121, pp. 2360- 2370 ,(2004) , 10.1023/B:JOTH.0000024617.88286.F2