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Algebro — Geometric applications of schur s- and q-polynomials

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Topics in Invariant Theory

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References

  1. I.N. Bernstein, I.M. Gel'fand, S.I. Gel'fand, Schubert cells and cohomology of the spaces G/P, Russian Math.Surv. 28, 1–26 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Berele, A. Regev, Hook Young diagrams with applications to combinatorics and to representation theory of Lie superalgebras, Adv. in Math., 64, 118–175 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  3. E.Cartan, The Theory of Spinors, Hermann (1966).

    Google Scholar 

  4. M. Demazure, Désingularisation des variétés de Schubert géneralisées, Ann. scient. Éc. Norm. Sup. t. 7, 53–88 (1974).

    MathSciNet  MATH  Google Scholar 

  5. K.G. Fischer, Symmetric polynomials and Hall's theorem, Discrete Math., 69,225–234 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  6. W.Fulton, Intersection Theory, Springer Verlag (1984).

    Google Scholar 

  7. I.M. Gel'fand, A.V. Zelevinsky, Models of representations of classical groups, Functional Analysis and Its Applications, vol.18, no.3, 14–31 (1984).

    MathSciNet  Google Scholar 

  8. J. Harris, L. Tu, Chern numbers of kernel and cokernel bundles, Inv. Math. 75, 467–475 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  9. S.Helgason, Differential Geometry and Symmetric Spaces, Academic Press (1962).

    Google Scholar 

  10. H. Hiller, B. Boe, Pieri formula for SO2n+1/Un and Spn/Un, Adv. in Math. 62, 49–67 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  11. P.N.Hoffman, J.F. Humhreys, a forthcoming book on Projective Representations of Symmetric Groups.

    Google Scholar 

  12. T.Józefiak, P.Pragacz, A determinantal formula for skew Q-functions, to appear.

    Google Scholar 

  13. T. Józefiak, A. Lascoux, P. Pragacz, Classes of determinantal varieties associated with symmetric and antisymmetric matrices, Izwiestja AN SSSR 45,no 9, 662–673, (1981).

    MATH  Google Scholar 

  14. R.C.King, S-functions and characters of Lie algebras and superalgebras, preprint, University of Southampton (1988).

    Google Scholar 

  15. S. Kerov, A. Vershik, The characters of the infinite symmetric group, Siam.J.Alg.Disc.Math., 7, 116–123 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  16. V. Lakshmibai, C.S. Seshadri, Geometry of G/P II, Proc.Indian Acad.Sci. A 87,1–54 (1978).

    MathSciNet  MATH  Google Scholar 

  17. A. Lascoux, La résultante de deux polynômes, Séminaire d'Algèbre Dubreil-Malliavin, Springer Lecture Notes 1220, 56–72 (1986).

    MathSciNet  Google Scholar 

  18. A. Lascoux, P. Pragacz, S-function series, J.Physics A Math. Gen. 21, 4105–4114 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  19. A. Lascoux, P.Pragacz, Schubert polynomials and ideals generated by symmetric functions, in preparation.

    Google Scholar 

  20. A.Lascoux, M.P.Schützenberger, Formulaire raisonné de fonctions symétriques, prepublication de l'Universite Paris 7 (1985).

    Google Scholar 

  21. A. Lascoux, M.P. Schützenberger, Symmetrization operators on polynonomial rings, Functional Analysis and Its Applications, 21, no.4, 77–78 (1987).

    MATH  Google Scholar 

  22. I.G.Macdonald, Symmetric functions and Hall polynomials, Oxford Univ. Press (1979).

    Google Scholar 

  23. A. Morris, On Q-functions, J.London Math.Soc. 37,no.148, 445–455 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  24. A. Morris, A note on the multiplication of Hall functions, J.London Math.Soc. 39,481–488 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  25. T.Muir, History of determinants, 5 volumes, Dover reprints (1960).

    Google Scholar 

  26. M.A.Nazarov, Factor-representations of the infinite spinsymmetric group, preprint, Moscow State University (1987).

    Google Scholar 

  27. E. Pomey, Sur le plus grand common diviseur de deux polynômes, Nouv. Ann. Math. (3) 7, 66–90, 407–427 (1888).

    MATH  Google Scholar 

  28. P. Pragacz, Determinantal varieties and symmetric polynomials, Functional Analysis and Its Applications,21,no.3,89–90 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  29. P. Pragacz, A note on elimination theory, Indagationes Math. 49 (2), 215–221 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  30. P. Pragacz, Enumerative geometry of degeneracy loci, Ann.Éc.Norm.Sup. vol.3, 413–454 (1988).

    MathSciNet  MATH  Google Scholar 

  31. J.B. Remmel, The combinatorics of (k,ℓ)-hook Schur functions, Contemporary Mathematics, 34, 253–287 (1984).

    Article  MathSciNet  Google Scholar 

  32. B. Sagan, Shifted tableaux,Schur Q-functions and a conjecture of Stanley, J.Combin.Theory Ser. A 45, 62–103 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  33. I. Schur, Uber die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen, J.Reine Angew. Math. 139, 155–250 (1911).

    MathSciNet  MATH  Google Scholar 

  34. A. Sergeev, Representations of Lie superalgebras gl(n/m) and Q(n) in the space of tensors, Functional Analysis and Its Applications t.18. no.1, 80–81 (1984).

    Article  MathSciNet  Google Scholar 

  35. A.Sergeev, Letter to the author, January 9 (1988).

    Google Scholar 

  36. G. Sokolov, Die Runft der Fuge durch Serrn Johann Gebaftian Bach ehemahligen Eapellmeifter und Mufikdirector ju Leipjig, Melodia, Moscow (1982).

    Google Scholar 

  37. R.P.Stanley, Problem 4 in Problem Session, Combinatorics and Algebra, Contemporary Mathematics, vol.34 (1984).

    Google Scholar 

  38. J. Stembridge, A characterization of supersymmetric polynomials J. Algebra, 95, 439–444 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  39. J. Stembridge, Shifted tableaux and the projective representations of the symmetric group, Adv. Math. to appear.

    Google Scholar 

  40. E. Thoma, Die unzerlegbaren positiv-definieren Klassenfunktionen der abzahlbar unendlichen symmetrischen Gruppe, Math. Zeit., 85, 40–61 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  41. N.Trudi, Teoria de Determinanti, Napoli (1862).

    Google Scholar 

  42. D.R.Worley,A theory of shifted Young tableaux,Ph.D. thesis, M.I.T. (1984).

    Google Scholar 

  43. Y.You, Polynomial solutions of the BKP hierarchy and projective representations of symmetric groups, preprint, M.I.T. (1988).

    Google Scholar 

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Authors
  1. Piotr Pragacz
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© 1991 Springer-Verlag

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Pragacz, P. (1991). Algebro — Geometric applications of schur s- and q-polynomials. In: Topics in Invariant Theory. Lecture Notes in Mathematics, vol 1478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083503

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  • DOI: https://doi.org/10.1007/BFb0083503

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  • Print ISBN: 978-3-540-54377-0

  • Online ISBN: 978-3-540-47592-7

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