Hostname: page-component-84b7d79bbc-rnpqb Total loading time: 0 Render date: 2024-07-30T17:46:33.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Perverse Sheaves on Grassmannians

Published online by Cambridge University Press:  20 November 2018

Tom Braden
Tom Braden*
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA, email: braden@math.umass.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We compute the category of perverse sheaves on Hermitian symmetric spaces in types $\text{A}$ and $\text{D}$, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety $\Lambda$.

Keywords

32S6032C3835A27perverse sheavesmicrolocal geometry
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 3 , 01 June 2002 , pp. 493 - 532
Copyright
Copyright © Canadian Mathematical Society 2002

References

[1] Andronikov, E., A microlocal version of the Riemann-Hilbert correspondence. Top. Appl. Meth. Nonlin. Anal. 4 (1994), 417–425.Google Scholar
[2] Beilinson, A. and Bernstein, J., Localisation de g-modules. C. R. Acad. Sci. Paris 292 (1981), 15–18.Google Scholar
[3] Beilinson, A., Ginzburg, V. and Sörgel, W., Koszul duality patterns in representation theory. J. Amer. Math. Soc. 9 (1996), 473–527.Google Scholar
[4] Boe, B. and Fu, J., Characteristic cycles associated to Schubert varieties in classical Hermitian symmetric spaces. Canad. J. Math. 49 (1997), 417–467.Google Scholar
[5] Braden, T., On the reducibility of characteristic varieties. Proc. Amer. Math. Soc., to appear.Google Scholar
[6] Braden, T. and Grinberg, M., Perverse sheaves on rank stratifications. Duke Math. J. 96 (1999), 317–362.Google Scholar
[7] Braden, T. and Khovanov, M., in preparation.Google Scholar
[8] Bressler, P., Finkelberg, M. and Lunts, V., Vanishing Cycles on Grassmannians. Duke Math. J. 61 (1990), 763–777.Google Scholar
[9] Fulton, W., Young Tableaux. Cambridge University Press, 1997.Google Scholar
[10] Galligo, A., Granger, M. and Maisonobe, P., D-modules et faisceaux pervers dont le support singulier est un croisement normal. Ann. Inst. Fourier 35 (1985), 1–48.Google Scholar
[11] Gel’fand, S., MacPherson, R. and Vilonen, K., Microlocal perverse sheaves. In preparation.Google Scholar
[12] Goresky, M. and MacPherson, R., Stratified Morse Theory. Springer, 1988.Google Scholar
[13] Kashiwara, M., Systems of microdifferential equations. Birkhauser, 1983.Google Scholar
[14] Kashiwara, M., Introduction to microlocal analysis. Enseign.Math. 32 (1986), 227–259.Google Scholar
[15] Kashiwara, M. and Kawai, T., On holonomic systems of microdifferential equations III. Publ. Res. Inst. Math. Sci. 17 (1981), 813–979.Google Scholar
[16] Kashiwara, M. and Schapira, P., Sheaves on Manifolds. Springer, 1990.Google Scholar
[17] Khovanov, M., Functor-valued invariants of tangles. Preprint, math.QA/0103190.Google Scholar
[18] Lascoux, A. and Schutzenberger, P., Polynômes de Kazhdan et Lusztig pour les Grassmanniennes. Astérisque 87–88 (1981), 249–266.Google Scholar
[19] MacPherson, R. and Vilonen, K., Elementary construction of perverse sheaves. Invent.Math. 84 (1986), 403–435.Google Scholar
[20] Massey, D., The Sebastiani-Thom isomorphism in the derived category. Comp.Math. 125 (2001), 353–362.Google Scholar
[21] Sebastiani, M. and Thom, R., Un résultat sur la monodromie. Invent.Math. 13 (1971), 90–96.Google Scholar
[22] Verdier, J.-L., Prolongement des faisceaux pervers monodromiques. Astérisque 130 (1985), 218–236.Google Scholar