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Schur Q-functions and cohomology of isotropic Grassmannians

Published online by Cambridge University Press:  24 October 2008

Tadeusz Józefiak
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Chopina 12, 87-100 Toruń, Poland

Abstract

We prove that for homogeneous spaces of isotropic Grassmannians the Borel map sends the basis of a truncated algebra of Schur Q-functions consisting of Q-functions or P-functions (depending on a case) onto the basis dual to the basis of Schubert cycles.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Bernstein, I. N., Gelfand, I. M. and Gelfand, S. I.. Schubert cells and cohomology of the spaces G/P. Math. Surveys 28 (1973), 326 (in Russian).CrossRefGoogle Scholar
[2]Demazure, M.. Invariants symétrique des groupes de Weyl et torsion. Invent. Math. 21 (1973), 287301.CrossRefGoogle Scholar
[3]Hiller, H.. Combinatorics and intersection of Schubert varieties. Comment. Math. Helv. 57 (1982), 4159.CrossRefGoogle Scholar
[4]Hiller, H. and Boe, B.. Pieri formula for SO2n+1/Un and Spn/Un. Advances in Math. 62 (1986), 4967.CrossRefGoogle Scholar
[5]Józeflak, T.. Characters of projective representations of symmetric groups. Expo. Math. 7 (1989), 193247.Google Scholar
[6]Macdonald, I. G.. Symmetric functions and Hall polynomials. Clarendon Press, Oxford, 1979.Google Scholar
[7]Morris, A. O.. A note on multiplication of Hall functions. J. London Math. Soc. 39 (1964), 481488.CrossRefGoogle Scholar
[8]Pragacz, P.. Algebro-geometric applications of Schur S- and Q-polynomials. Seminaire d'algèbre Dubreil-Malliavin (to appear).Google Scholar
[9]Schur, I.. Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Sustitutionen. J. Reine Angew. Math. 139 (1911), 155250.Google Scholar
[10]Stembridge, J. R.. Shifted tableaux and the projective representations of symmetric groups. Advances in Math. 74 (1989), 87134.CrossRefGoogle Scholar