Koszul duality patterns in representation theory

Journal of the American Mathematical Society

Volumn 9, Issue 2, 1996, Pages 473-527

  Beilinson, Alexander ^a   Ginzburg, Victor ^b   Soergel, Wolfgang ^c,d  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

^c MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

^d UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030528385     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-96-00192-0     Document Type: Article

References (39)

1. Jeffrey Adams, Dan Barbasch, and David A. Vogan, Jr, The Langlands classification and irreducible characters for real reductive groups, Progress in Mathematics, vol. 104, Birkhäuser, 1992. MR 93j:22001
2. Jörgen Backelin, A distributiveness property of augmented algebras and some related homological results, Ph. D. Thesis, Stockholm, 1982.
3. Dan Barbasch, Filtrations on Verma modules, Ann. Scient. Éc. Norm. Sup. 16 (1983), 489-494. MR 85j:17013
4. Hyman Bass, Algebraic K-theory, Benjamin, 1968. MR 40:2736
5. Alexander A. Beilinson and Joseph N. Bernstein, Localisation de g-modules, C. R. Acad. Sci. Paris, Sér. 1 292 (1981), 15-18. MR 82k:14015
6. Alexander A. Beilinson and Joseph N. Bernstein, A proof of Jantzen conjectures, Preprint, 1986; finally published in I. M. Gelfand Seminar, Advances in Soviet Math., vol. 16, part 1, Amer. Math. Soc., Providence, RI, 1993, pp. 1-50. MR 95a:22022
7. Alexander A. Beilinson and Joseph N. Bernstein, A proof of Jantzen conjectures, Preprint, 1986; finally published in I. M. Gelfand Seminar, Advances in Soviet Math., vol. 16, part 1, Amer. Math. Soc., Providence, RI, 1993, pp. 1-50. MR 95a:22022
8. Alexander A. Beilinson, Joseph N. Bernstein, and Pierre Deligne, Faisceaux pervers, Astérisque 100 (1982). MR 86g:32015
9. Arnault Beauville, Variétés kähleriennes dont la première classe de Chern est nulle, J. Diff. Geometry 18 (1983), 755-782. MR 86c:32030
10. Joseph N. Bernstein, Trace in categories, Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory (Alain Connes, Michel Duflo, Anthony Joseph, and Rudolph Rentschler, eds.), Birkhäuser, 1990, pp. 417-423. MR 92d:17010
11. Jörgen Backelin and Ralf Fröberg, Koszul algebras, Veronese subrings and rings with linear resolutions, Rev. Roumaine Math. Pures Appl. 30 (1985), 85-97. MR 87c:16002
12. Joseph N. Bernstein and Sergei I. Gelfand, Tensor products of finite and infinite representations of semisimple Lie algebras, Compositio Math. 41 (1980), 245-285. MR 82c:17003
13. Alexander A. Beilinson and Victor Ginsburg, Mixed categories, Ext-duality and representations (results and conjectures), Preprint, 1986.
14. Joseph N. Bernstein, Israel M. Gelfand, and Sergei I. Gelfand, Schubert cells and cohomology of the spaces G/P, Russian Math. Surveys 28 (1973), no. 3, 1-26. MR 55:2941
15. n and problems of linear algebra, Functional Analysis and its App. 12 (1978), no. 3, 214-216. MR 80c:14010a
16. Alexander A. Beilinson, Victor Ginsburg, and Vadim V. Schechtman, Koszul duality, Journal of Geometry and Physics 5 (1988), 317-350. MR 91c:18011
17. Alexander Beilinson, Robert MacPherson, and Vadik Schechtmann, Notes on motivic cohomology, Duke Math. Journal 54 (1987), 679-710. MR 88f:14021
18. Armand Borel (ed.), Intersection cohomology, Progress in Mathematics, vol. 50, Birkhäuser, 1984. MR 88d:32024
19. Luis G. Casian and David H. Collingwood, The Kazhdan-Lusztig conjecture for generalized Verma modules, Math. Z. 195 (1987), 581-600. MR 88i:17008
20. Edward Cline, Brian Parshall, and Leonard Scott, Abstract Kazhdan-Lusztig theories, Tôhoku Math. J. (2) 45 (1993), 511-534. MR 94k:20079
21. Pierre Deligne, La conjecture de Weil II, IHES Publ. Math. 52 (1980), 137-252. MR 83c:14017
22. Tom J. Enright and Brad Shelton, Categories of highest weight modules: Applications to classical hermitian symmetric pairs, Memoirs of the AMS 367 (1987). MR 88f:22052
23. Robin Hartshorne, Residues and duality, Lecture Notes in Mathematics, vol. 20, Springer, 1966. MR 36:5145
24. Ron S. Irving, The socle filtration of a Verma module, Ann. Scient. Éc. Norm. Sup. 21 (1988), 47-65. MR 89h:17015
25. s and applications, Memoirs of the AMS 419 (1990). MR 90f:17011
26. Jens C. Jantzen, Representations of algebraic groups, Pure and Applied Mathematics, vol. 131, Academic Press, 1987. MR 89c:20001
27. Bernhard Keller, Deriving DG-categories, Ann. Sci. École Norm. Sup. (4) 27 (1994), 63-102. MR 95e:18010
28. David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Inventiones Math. 53 (1980), 191-213. MR 81j:20066
29. David Kazhdan and George Lusztig, Schubert varieties and Poincaré duality, Proc. Symp. Pure Math. 36, AMS, 1980, pp. 185-203. MR 84g:14054
30. Masaki Kashiwara and Pierre Schapira, Sheaves on manifolds, Grundlehren, vol. 292, Springer, 1990. MR 92a:58132
31. Clas Löfwall, On the subalgebra generated by the one-dimensional elements in the Yoneda ext-algebra, Lecture Notes in Mathematics, vol. 1183, Springer, 1986, pp. 291-338. MR 88f:16030
32. e série 20 (1987), 311-324. MR 89e:32017
33. Stewart B. Priddy, Koszul resolutions, Transactions AMS 152 (1970), 39-60. MR 42:346
34. Morihiko Saito, Mixed Hodge modules, Publications RIMS, Kyoto University 26 (1990), 221-333. MR 91m:14014
35. Wolfgang Soergel, Équivalences de certaines catégories de g-modules, C. R. Acad. Sci. Paris, Sér. 1 303 (1986), no. 15, 725-728. MR 88c:17011
36. Wolfgang Soergel, n-cohomology of simple highest weight modules on walls and purity, Inventiones Math. 98 (1989), 565-580. MR 90m:22037
37. Wolfgang Soergel, Parabolisch-singuläre Dualität für Kategorie script O sign, Preprint MPI/89-68, 1989.
38. Wolfgang Soergel, Kategorie script O sign, perverse Garben und Moduln, über den Koinvarianten zur Weylgruppe, Journal of the AMS 3 (1990), 421-445. MR 91e:17007
39. Wolfgang Soergel, Langlands' philosophy and Koszul duality, Preprint, 1992.