Schubert polynomials for the classical groups

Billey, Sara; Haiman, Mark

doi:10.1090/S0894-0347-1995-1290232-1

Schubert polynomials for the classical groups
HTML articles powered by AMS MathViewer

by Sara Billey and Mark Haiman

J. Amer. Math. Soc. 8 (1995), 443-482

DOI: https://doi.org/10.1090/S0894-0347-1995-1290232-1

PDF | Request permission

References

I. N. Bernšteĭn, I. M. Gel′fand, and S. I. Gel′fand, Schubert cells, and the cohomology of the spaces $G/P$, Uspehi Mat. Nauk 28 (1973), no. 3(171), 3–26 (Russian). MR 0429933
N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
Sara C. Billey, William Jockusch, and Richard P. Stanley, Some combinatorial properties of Schubert polynomials, J. Algebraic Combin. 2 (1993), no. 4, 345–374. MR 1241505, DOI 10.1023/A:1022419800503
Michel Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup. (4) 7 (1974), 53–88 (French). MR 354697
Paul Edelman and Curtis Greene, Balanced tableaux, Adv. in Math. 63 (1987), no. 1, 42–99. MR 871081, DOI 10.1016/0001-8708(87)90063-6

Combinatorial

analogues of Schubert polynomials

Sergey Fomin and Richard P. Stanley, Schubert polynomials and the nil-Coxeter algebra, Adv. Math. 103 (1994), no. 2, 196–207. MR 1265793, DOI 10.1006/aima.1994.1009

Determinants and plane partitions

Mark D. Haiman, Dual equivalence with applications, including a conjecture of Proctor, Discrete Math. 99 (1992), no. 1-3, 79–113. MR 1158783, DOI 10.1016/0012-365X(92)90368-P
Steven L. Kleiman, Problem 15: rigorous foundation of Schubert’s enumerative calculus, Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Northern Illinois Univ., De Kalb, Ill., 1974) Proc. Sympos. Pure Math., Vol. XXVIII, Amer. Math. Soc., Providence, R.I., 1976, pp. 445–482. MR 0429938
S. L. Kleiman and Dan Laksov, Schubert calculus, Amer. Math. Monthly 79 (1972), 1061–1082. MR 323796, DOI 10.2307/2317421
Alain Lascoux and Marcel-Paul Schützenberger, Polynômes de Schubert, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 13, 447–450 (French, with English summary). MR 660739
I. G. Macdonald, Schubert polynomials, Surveys in combinatorics, 1991 (Guildford, 1991) London Math. Soc. Lecture Note Ser., vol. 166, Cambridge Univ. Press, Cambridge, 1991, pp. 73–99. MR 1161461
I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979. MR 553598
Piotr Pragacz, Algebro-geometric applications of Schur $S$- and $Q$-polynomials, Topics in invariant theory (Paris, 1989/1990) Lecture Notes in Math., vol. 1478, Springer, Berlin, 1991, pp. 130–191. MR 1180989, DOI 10.1007/BFb0083503
Bruce E. Sagan, Shifted tableaux, Schur $Q$-functions, and a conjecture of R. Stanley, J. Combin. Theory Ser. A 45 (1987), no. 1, 62–103. MR 883894, DOI 10.1016/0097-3165(87)90047-1
Richard P. Stanley, On the number of reduced decompositions of elements of Coxeter groups, European J. Combin. 5 (1984), no. 4, 359–372. MR 782057, DOI 10.1016/S0195-6698(84)80039-6
Richard P. Stanley, Some combinatorial aspects of the Schubert calculus, Combinatoire et représentation du groupe symétrique (Actes Table Ronde CNRS, Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976) Lecture Notes in Math., Vol. 579, Springer, Berlin, 1977, pp. 217–251. MR 0465880
Michelle L. Wachs, Flagged Schur functions, Schubert polynomials, and symmetrizing operators, J. Combin. Theory Ser. A 40 (1985), no. 2, 276–289. MR 814415, DOI 10.1016/0097-3165(85)90091-3

A theory of shifted Young tableaux