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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Schubert polynomials for the classical groups
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by Sara Billey and Mark Haiman PDF
J. Amer. Math. Soc. 8 (1995), 443-482 Request permission
References
    I. N. Bernstein, I. M. Gel’fand, and S. I. Gel’fand, Schubert cells and cohomology of the spaces $G/P$, Russian Math. Surveys 28 (1973), no. 3, 1-26. N. Bourbaki, Groupes et algebras de Lie, Chapitres 4, 5, 6, Hermann, Paris, 1968. S. C. Billey, W. Jockusch, and R. P. Stanley, Some combinatorial properties of Schubert polynomials, J. Algebraic Combin. 2 (1993), 345-374. M. Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup. 7 (1974), 53-88. P. Edelman and C. Greene, Balanced tableaux, Adv. Math. 63 (1987), 42-99. S. Fomin and A. N. Kirillov, Combinatorial ${B_n}$ analogues of Schubert polynomials, Manuscript, M.I.T., 1993. S. Fomin and R. P. Stanley, Schubert polynomials and the nilCoxeter algebra, Adv. Math. 103 (1994), 196-207. I. Gessel and G. Viennot, Determinants and plane partitions, preprint, 1983. M. Haiman, Dual equivalence with applications, including a conjecture of Proctor, Discrete Math. 99 (1992), 79-113. S. L. Kleiman, Problem 15. Rigorous foundation of Schubert’s enumerative caculus, Mathematical Developments Arising from Hilbert Problems (F. E. Browder, ed.), Proc. Sympos. Pure Math., vol. 28, Part II, Amer. Math. Soc., Providence, RI, 1976, pp. 445-482. S. L. Kleiman and D. Laksov, Schubert calculus, Amer. Math. Monthly 79 (1972), 1061-1082. A. Lascoux and M.-P. Schützenberger, Polynômes de Schubert, C. R. Acad. Sci. Paris 294 (1982), 447-450. I. G. Macdonald, Notes on Schubert polynomials, Publications du L.A.C.I.M., vol. 6, Université du Québec, Montréal, 1991. —, Symmetric functions and Hall polynomials, Oxford Univ. Press, London and New York, 1979. P. Pragacz, Algebro-geometric applications of Schur $S$- and $Q$-polynomials, Topics in Invariant Theory (M.-P. Malliavin, ed.), Lecture Notes in Math., vol. 1478, Springer-Verlag, Berlin and New York, 1991, pp. 130-191. B. E. Sagan, Shifted tableaux, Schur $Q$-functions, and a conjecture of R. Stanley, J. Combin. Theory Ser. A 45 (1987), 62-103. R. P. Stanley, On the number of reduced decompositions of elements of Coxeter groups, European J. Combin. 5 (1984), 359-372. —, Some combinatorial aspects of the Schubert calculus, Combinatoire et Représentation du Groupe Symétrique (Strasbourg, 1976) (D. Foata, ed.), Lecture Notes in Math., vol. 579, Springer-Verlag, Berlin and New York, 1977, pp. 217-251. M. Wachs, Flagged Schur functions, Schubert polynomials, and symmetrizing operators, J. Combin. Theory Ser. A 40 (1985), 276-289. D. R. Worley, A theory of shifted Young tableaux, Ph.D. Thesis, M.I.T., 1984.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 8 (1995), 443-482
  • MSC: Primary 05E15; Secondary 14M15
  • DOI: https://doi.org/10.1090/S0894-0347-1995-1290232-1
  • MathSciNet review: 1290232