Quelques applications de la cohomologie d'intersection

Springer, T. A.

Séminaire Bourbaki : volume 1981/82, exposés 579-596, Astérisque, no. 92-93 (1982), Exposé no. 589, 25 p.

MR 689533 | Zbl 0526.22014 | 11 citations dans Numdam

BibTeX
RIS

@incollection{SB_1981-1982__24__249_0,
     author = {Springer, Tonny Albert},
     title = {Quelques applications de la cohomologie d'intersection},
     booktitle = {S\'eminaire Bourbaki : volume 1981/82, expos\'es 579-596},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:589},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {92-93},
     year = {1982},
     zbl = {0526.22014},
     mrnumber = {689533},
     language = {fr},
     url = {http://archive.numdam.org/item/SB_1981-1982__24__249_0/}
}

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TI  - Quelques applications de la cohomologie d'intersection
BT  - Séminaire Bourbaki : volume 1981/82, exposés 579-596
AU  - Collectif
T3  - Astérisque
N1  - talk:589
PY  - 1982
DA  - 1982///
IS  - 92-93
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/SB_1981-1982__24__249_0/
UR  - https://zbmath.org/?q=an%3A0526.22014
UR  - https://www.ams.org/mathscinet-getitem?mr=689533
LA  - fr
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ER  -

Springer, T. A. Quelques applications de la cohomologie d'intersection, dans Séminaire Bourbaki : volume 1981/82, exposés 579-596, Astérisque, no. 92-93 (1982), Exposé no. 589, 25 p. http://archive.numdam.org/item/SB_1981-1982__24__249_0/

Bibliographie
Cité par

[1] A. Alexeevsky, Groupe de composantes de centralisateurs d'éléments unipotents dans les groupes algébriques semi-simples (en russe), Publ. Inst. Math. Tbilisi 52(1979), 5-27.

[2] A. Beilinson - J. Bernstein, Localisation de $g$ -modules, C.R. Acad. Sc. Paris 292(1981), 15-18. | MR 610137 | Zbl 0476.14019

[3] C. T. Benson - C. W. Curtis, On the degrees and rationality of certain characters of finite Chevalley groups, Trans. Amer. Math. Soc. 165(1972), 251-273 et 202(1975), 405-406. | MR 304473 | Zbl 0246.20008

[4] A. Borel et al., Seminar on algebraic groups and related finite groups, Lect. Notes in Math. vol. 131, Springer-Verlag,1970. | MR 258838 | Zbl 0192.36201

[5] W. Borho - H. Kraft, Uber Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen, Comm. Math. Helv. 54(1976), 61-104. | MR 522032 | Zbl 0395.14013

[6] W. Borho - R. Macpherson, Représentations des groupes de Weyl et homologie d'intersection pour les variétés de nilpotents, C.R. Acad. Sc. Paris., 292(1981), 707-710. | MR 618892 | Zbl 0467.20036

[7] N. Bourbaki, Groupes et algèbres de Lie, Chap. IV, V, VI, Hermann, Paris, 1968. | MR 240238 | Zbl 0483.22001

[ 8] E. Brieskorn, Singular elements of semisimple algebraic groups,Actes Congrès Intern. Math. 1970 t.2, 279-284. | MR 437798 | Zbl 0223.22012

[9] J.-L. Brylinski, Differential operators on the flag varieties, dans : Tableaux de Young..., Astérisque, vol. 87-88(1982), 43-60. | MR 646814 | Zbl 0537.14010

[10] J.-L. Brylinski, (Co) homologie d'intersection et faisceaux pervers, Sém. Bourbaki 1981/82, exposé n° 585, Astérisque 92-93(1982), 129-157. | EuDML 109985 | Numdam | MR 689529 | Zbl 0574.14017

[11] J.-L. Brylinski - M. Kashiwara, Kazhdan - Lusztig conjecture and holonomic systems, Inv. Math. 64(1981), 387-410. | EuDML 142827 | MR 632980 | Zbl 0473.22009

[12] M. Demazure, Invariants symétriques des groups de Weyl et torsion, Inv. Math. 21(1973), 287-301. | EuDML 142233 | MR 342522 | Zbl 0269.22010

[13] M. Demazure, Désingularisation des variétés de Schubert, Ann. Ec. Norm. Sup. (4) 7(1974), 53-88. | EuDML 81930 | Numdam | MR 354697 | Zbl 0312.14009

[14] V. V. Deodhar, Some characterizations of Bruhat ordening on a Coxeter group and determination of the relative Möbius function, Inv. Math. 39(1977), 187-198. | EuDML 142465 | MR 435249 | Zbl 0346.20032

[15] V. V. Deodhar, On the Kazhdan-Lusztig conjecture, Proc. Kon. Ak. v. Wet., Amsterdam, A 86(1982), 1-17. | MR 653451 | Zbl 0486.17004

[16] O. Gabber - A. Joseph, Towards the Kazhdan-Lusztig conjecture, Ann. Ec. Norm. Sup. 14(1981), 261-302. | EuDML 82075 | Numdam | MR 644519 | Zbl 0476.17005

[17] S. Gelfand - R. Macpherson, Verma modules and Schubert cells: a dictionary, Sém. d'Algèbre P. Dubreil-M.-P. Malliavin 1981, Lect. Notes in Math., vol. 924, Springer-Verlag, 1982. | MR 662251 | Zbl 0512.22009

[18] M. Goresky - R. Macpherson, Intersection homology II, à paraître dans Inv. Math.. | EuDML 143014 | Zbl 0529.55007

[19] H. Grauert - O. Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen, Inv. Math. 11(1970), 263-292. | EuDML 142056 | MR 302938 | Zbl 0202.07602

[20] A. Grothendieck, Local cohomology, Lect. Notes in Math. vol. 41, Springer-Verlag, 1967. | MR 224620 | Zbl 0185.49202

[21] W. Hesselink, Cohomology and the resolution of the nilpotent variety, Math. Ann. 223(1976), 249-252. | EuDML 162889 | MR 417195 | Zbl 0318.14007

[22] R. Hotta, On Springer's representations, J. Fac. Sci. Univ. Tokyo 28(1982), 863-876. | MR 656061 | Zbl 0584.20033

[23] R. Hotta - T. A. Springer, A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups, Inv. Math. 41(1977), 113-127. | EuDML 142488 | MR 486164 | Zbl 0389.20037

[24] J. C. Jantzen, Moduln mit einem höchsten Gewicht, Lect. Notes in Math. vol. 750, Springer-Verlag, 1979. | MR 552943 | Zbl 0426.17001

[25] M. Kashiwara, B-functions and holonomic systems, Inv. Math. 38(1976), 33-54. | EuDML 142441 | MR 430304 | Zbl 0354.35082

[26] D. Kazhdan - G. Lusztig, Representations of Coxeter groups and Hecke algebras, Inv. Math. 53(1979), 165-184. | EuDML 142660 | MR 560412 | Zbl 0499.20035

[27] D. Kazhdan - G. Lusztig, Schubert varieties and Poincaré duality, Proc. Symp. Pure Math. vol. 36, 185-203, Amer. Math. Soc. 1980. | MR 573434 | Zbl 0461.14015

[28] D. Kazhdan - G. Lusztig, A topological approach to Springer's representations, Adv. in Math. 38(1980), 222-228. | MR 597198 | Zbl 0458.20035

[29] G. Kempf, The Grothendieck-Cousin complex of an induced representation, Adv. in Math. 29(1978), 310-396. | MR 509802 | Zbl 0393.20027

[30] G. Kempf et al., Toroidal embeddings I, Lect. Notes in Math. vol. 339, Springer-Verlag, 1973. | MR 335518 | Zbl 0271.14017

[31] B. Kostant, Lie group representations in polynomial rings, Amer. J. Math. 85(1963), 327-404. | MR 158024 | Zbl 0124.26802

[32] A. Lascoux - M. Schützenberger, Polynômes de Kazhdan et Lusztig pour les Grassmanniennes, dans : Tableaux de Young..., Astérisque 87-88(1982), 249-266. | Zbl 0504.20007

[33] G. Lusztig, Some problems in the representation theory of finite Chevalley groups, Proc. Symp. Pure Math. vol. 37, 313-317, Amer. Math. Soc. 1980. | MR 604598 | Zbl 0453.20005

[34] G. Lusztig, On a theorem of Benson and Curtis, J. Alg. 71(1981), 490-498. | MR 630610 | Zbl 0465.20042

[35] G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. in Math. 42 (1981), 169-178. | MR 641425 | Zbl 0473.20029

[36] G. Lusztig, Singularities, character formulas and a q-analog of weight multiplicities, à paraître dans Comptes-Rendus Conf. sur la th. des singularités (Luminy, 1981). | Zbl 0561.22013

[37] G. Lusztig, Unipotent characters of the symplectic and odd orthogonal groups over a finite field, Inv. Math. 64(1981), 263-296. | EuDML 142823 | MR 629472 | Zbl 0477.20023

[38] G. Lusztig, Unipotent characters of the even orthogonal groups over a finite field, à paraître dans Trans. Amer. Math. Soc. | MR 662064 | Zbl 0491.20034

[39] G. Lusztig - D. Vogan, Singularities of closures of K-orbits on flag manifolds, à paraître. | Zbl 0544.14035

[40] I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Univ. Press, 1979. | MR 553598 | Zbl 0899.05068

[41] Z. Mebkhout, Une autre équivalence de catégoriés, à paraître.

[42] F. Rodier, Représentations de GL(n,k) où k est un corps p-adique, Sém. Bourbaki 1981/82, exposé n° 587, Astérisque 92-93(1982), 201-218. | EuDML 109988 | Numdam | MR 689531 | Zbl 0506.22019

[43] T. Shoji, On the Springer representations of the Weyl groups of classical algebraic groups, Comm. Alg. 7(1979), 1713-1745 et 2027-2033. | MR 546195 | Zbl 0423.20042

[44] P. Slodowy, Four lectures on simple groups and singularities, Comm. Math. Inst. Utrecht, 1980. | MR 563725 | Zbl 0425.22020

[45] P. Slodowy, Simple singularities and simple algebraic groups, Lect. Notes in Math. vol. 815, Springer-Verlag, 1980. | MR 584445 | Zbl 0441.14002

[46] N. Spaltenstein, The fixed point set of a unipotent transformation on the flag manifold, Proc. Kon. Ak. Wet. Amsterdam 79(1976), 452-456. | MR 485901 | Zbl 0343.20029

[47] T. A. Springer, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Inv. Math. 36(1976), 173-207. | EuDML 142418 | MR 442103 | Zbl 0374.20054

[48] T. A. Springer, Linear algebraic groups, Birkhäuser, 1981. | MR 632835 | Zbl 0453.14022

[49] B. Srinivasan, Representations of finite Chevalley groups, Lect. Notes in Math. vol. 764, Springer-Verlag, 1979. | MR 551499 | Zbl 0434.20022

[50] R. Steinberg, On the desingularization of the unipotent variety, Inv. Math. 36(1976), 209-224. | MR 430094 | Zbl 0352.20035

[51] J.-L. Verdier, Stratifications de Whitney et théorème de Bertini-Sard, Inv. Math. 36(1976), 295-312. | MR 481096 | Zbl 0333.32010

[52] D. A. Vogan, Jr, Irreducible characters of semisimple Lie groups III, Proof of Kazhdan-Lusztig conjecture in the integral case, preprint M.I.T. | MR 689650

[53] A. V. Zelevinsky, Un analogue p-adique de la conjecture de Kazhdan-Lusztig (en russe), Funktion. Anal. 15(1981), 9-21. | MR 617466 | Zbl 0463.22013