Perverse Sheaves on Grassmannians
Canadian journal of mathematics, Tome 54 (2002) no. 3, pp. 493-532

Voir la notice de l'article provenant de la source Cambridge University Press

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 $\Lambda$ .
DOI : 10.4153/CJM-2002-017-6
Mots-clés : 32S60, 32C38, 35A27, perverse sheaves, microlocal geometry
Braden, Tom. Perverse Sheaves on Grassmannians. Canadian journal of mathematics, Tome 54 (2002) no. 3, pp. 493-532. doi: 10.4153/CJM-2002-017-6
@article{10_4153_CJM_2002_017_6,
     author = {Braden, Tom},
     title = {Perverse {Sheaves} on {Grassmannians}},
     journal = {Canadian journal of mathematics},
     pages = {493--532},
     year = {2002},
     volume = {54},
     number = {3},
     doi = {10.4153/CJM-2002-017-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2002-017-6/}
}
TY  - JOUR
AU  - Braden, Tom
TI  - Perverse Sheaves on Grassmannians
JO  - Canadian journal of mathematics
PY  - 2002
SP  - 493
EP  - 532
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2002-017-6/
DO  - 10.4153/CJM-2002-017-6
ID  - 10_4153_CJM_2002_017_6
ER  - 
%0 Journal Article
%A Braden, Tom
%T Perverse Sheaves on Grassmannians
%J Canadian journal of mathematics
%D 2002
%P 493-532
%V 54
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2002-017-6/
%R 10.4153/CJM-2002-017-6
%F 10_4153_CJM_2002_017_6

[1] [1] Andronikov, E., A microlocal version of the Riemann-Hilbert correspondence. Top. Appl. Meth. Nonlin. Anal. 4 (1994), 417–425. Google Scholar

[2] [2] Beilinson, A. and Bernstein, J., Localisation de g-modules. C. R. Acad. Sci. Paris 292 (1981), 15–18. Google Scholar

[3] [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] [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] [5] Braden, T., On the reducibility of characteristic varieties. Proc. Amer. Math. Soc., to appear. Google Scholar

[6] [6] Braden, T. and Grinberg, M., Perverse sheaves on rank stratifications. Duke Math. J. 96 (1999), 317–362. Google Scholar

[7] [7] Braden, T. and Khovanov, M., in preparation. Google Scholar

[8] [8] Bressler, P., Finkelberg, M. and Lunts, V., Vanishing Cycles on Grassmannians. Duke Math. J. 61 (1990), 763–777. Google Scholar

[9] [9] Fulton, W., Young Tableaux. Cambridge University Press, 1997. Google Scholar

[10] [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] [11] Gel’fand, S., MacPherson, R. and Vilonen, K., Microlocal perverse sheaves. In preparation. Google Scholar

[12] [12] Goresky, M. and MacPherson, R., Stratified Morse Theory. Springer, 1988. Google Scholar

[13] [13] Kashiwara, M., Systems of microdifferential equations. Birkhauser, 1983. Google Scholar

[14] [14] Kashiwara, M., Introduction to microlocal analysis. Enseign.Math. 32 (1986), 227–259. Google Scholar

[15] [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] [16] Kashiwara, M. and Schapira, P., Sheaves on Manifolds. Springer, 1990. Google Scholar

[17] [17] Khovanov, M., Functor-valued invariants of tangles. Preprint, math.QA/0103190. Google Scholar

[18] [18] Lascoux, A. and Schutzenberger, P., Polynômes de Kazhdan et Lusztig pour les Grassmanniennes. Astérisque 87–88 (1981), 249–266. Google Scholar

[19] [19] MacPherson, R. and Vilonen, K., Elementary construction of perverse sheaves. Invent.Math. 84 (1986), 403–435. Google Scholar

[20] [20] Massey, D., The Sebastiani-Thom isomorphism in the derived category. Comp.Math. 125 (2001), 353–362. Google Scholar

[21] [21] Sebastiani, M. and Thom, R., Un résultat sur la monodromie. Invent.Math. 13 (1971), 90–96. Google Scholar

[22] [22] Verdier, J.-L., Prolongement des faisceaux pervers monodromiques. Astérisque 130 (1985), 218–236. Google Scholar

Cité par Sources :