Translation and shuffling of projectively presentable modules and a categorification of a parabolic hecke module

Transactions of the American Mathematical Society

Volumn 357, Issue 7, 2005, Pages 2939-2973

  Mazorchuk, Volodymyr ^a   Stroppel, Catharina ^b,c  

^a UPPSALA UNIVERSITY   (Sweden)

^b AARHUS UNIVERSITY   (Denmark)

^c UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22544463624     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-04-03650-5     Document Type: Article

References (38)

1. [AJS] H. H. Andersen, J. C. Jantzen, W. Soergel, Representations of quantum groups at a pth root of unity and of semisimple groups in characteristic p: independence of p. Astérisque No. 220 (1994). MR95j:20036
2. [AL] H. H. Andersen, N. Lauritzen, Twisted Verma modules, in: Studies in Memory of Issai Schur, 1-26, v. 210, Progress in Math., Birkhäuser, Basel, 2002. MR2004d:17005
3. [Au] M. Auslander, Representation theory of Artin algebras I. Commun, in Alg. 1 (1974), 177-268. MR50:2240
4. [Ba] E. Backelin, The Hom-spaces between protective functors. Represent. Theory 5 (2001), 267-283 (electronic). MR2002f:17007
5. [Be] I. N. Bernstein, Trace in categories. Operator algebras, unitary representations, enveloping algebras, and invariant theory (Paris, 1989), 417-423, Progr. Math., 92, Birkhäuser Boston, Boston, MA, 1990. MR92d: 17010
6. 2) via protective and Zuckerman functors, Selecta Math. (N.S.), 5 (1999), no. 2, 199-241. MR2000i:17009
7. [BG] I. N. Bernstein, S. I. Gelfand, Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras. Compositio Math. 41 (1980), no. 2, 245-285. MR82c:17003
8. [BGG] I. N. Bernstein, I. M. Gelfand, S. I. Gelfand, A certain category of g-modules. Funkcional. Anal, i Prilozen. 10 (1976), no. 2, 1-8. MR53:10880
9. [BGS] A. Beilinson, V. Ginzburg, W. Soergel, Koszul duality patterns in representation theory. J. Amer. Math. Soc. 9 (1996), no. 2, 473-527. MR96k:17010
10. [Bo] N. Bourbaki, Lie groups and Lie algebras. Chapters 4-6- Elements of Mathematics. Springer-Verlag, Berlin, 2002. MR2003a: 17001
11. [CPS] E. Cline, B. Parshall, L. Scott, Finite-dimensional algebras and highest weight categories. J. Reine Angew. Math. 391 (1988), 85-99. MR90d:18005
12. [CI] D. Collingwood, R. S. Irving, A decomposition theorem for certain self-dual modules in the category O. Duke Math. J. 58 (1989), no. 1, 89-102. MR90k:17010
13. [De] V. Deodhar, On some geometric aspects of Bruhat orderings. II. The parabolic analogue of Kazhdan-Lusztig polynomials. J. Algebra 111 (1987), no. 2, 483-506. MR89a:20054
14. [Di] J. Dixmier, Enveloping algebras. Graduate Studies in Mathematics, 11. American Mathematical Society, Providence, RI, 1996. MR97c: 17010
15. [Dl] V. Dlab, Properly stratified algebras. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000), no. 3, 191-196. MR2001e:16016
16. [DFO] Yu. Drozd, S. Ovsienko, V. Futorny, The Harish-Chandra S-homomorphism and script B sign-modules generated by a semiprimitive element. Ukrain. Mat. Zh. 42 (1990), no. 8, 1031-1037;
17. translation in Ukrainian Math. J. 42 (1990), no. 8, 919-924 (1991) MR92d:17003
18. [En] T. Enright, On the fundamental series of a real semisimple Lie algebra: their irreducibility, resolutions and multiplicity formulae. Ann. of Math. (2) 110 (1979), no. 1, 1-82. MR81a:17003
19. [FKM1] V. Futorny, S. König, V. Mazorchuk, Categories of induced modules and standardly stratified algebras. Algebr. Represent. Theory 5 (2002), no. 3, 259-276. MR2003g:17005
20. [FKM2] V. Futorny, S. König, V. Mazorchuk, S-subcategories in O. Manuscripta Math. 102 (2000), no. 4, 487-503. MR2001h:17022
21. [GJ] O. Gabber, A. Joseph, Towards the Kazhdan-Lusztig conjecture. Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 3, 261-302. MR83e:17009
22. [Hu] J. Humphreys, Reflection groups and Coxeter groups. Cambridge Studies in Advanced Mathematics, 29. Cambridge University Press, Cambridge, 1990. MR92h:20002
23. [Ir1] R. Irving, Shuffled Verma modules and principal series modules over complex semisimple Lie algebras. J. London Math. Soc. (2) 48 (1993), no. 2, 263-277. MR94i:17013
24. s: self-duality. Trans. Amer. Math. Soc. 291 (1985), no. 2, 701-732. MR87i:17005
25. [Ja] J. C. Jantzen, Einhüllende Algebren halbeinfacher Lie-Algebren. Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Springer-Verlag, Berlin, 1983. MR86c:17011
26. [Kh] O. Khomenko, Categories with protective functors, PhD thesis. Universität Freiburg (Germany), 2004.
27. [KL] D. Kazhdan, G. Lusztig, Representations of Coxeter groups and Hecke algebras. Invent. Math. 53 (1979), no. 2, 165-184. MR81j:20066
28. [KM1] S. König, V. Mazorchuk, Enright's completions and injectively copresented modules. Trans. Amer. Math. Soc. 354 (2002), no. 7, 2725-2743. MR2003c:17009
29. [KM2] S. König, V. Mazorchuk, An equivalence of two categories of sl(n, ℂ)-modules. Algebr. Represent. Theory 5 (2002), no. 3, 319-329. MR2003i:17009
30. [Ma] V. Mazorchuk, Twisted and shuffled filtrations on tilting modules. Math. Reports of the Academy of Science of the Royal Society of Canada 25 (2003), no. 1, 26-32. MR2004c:17013
31. [Rin] C. M. Ringel, The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences. Math. Z. 208 (1991), no. 2, 209-223. MR93c:16010
32. [Ric] J. Rickard, Translation functors and equivalences of derived categories for blocks of algebraic groups. Finite-dimensional algebras and related topics (Ottawa, ON, 1992), 255-264, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 424, Kluwer Acad. Publ., Dordrecht, 1994. MR95k:20068
33. [So1] W. Soergel, Kazhdan-Lusztig polynomials and combinatorics for tilting modules. Represent. Theory 1 (1997), 83-114 (electronic). MR98d:17026
34. [So2] W. Soergel, Kategorie O, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe. J. Amer. Math. Soc. 3 (1990), no. 2, 421-445. MR91e:17007
35. [So3] W. Soergel, Équivalences de certaines catégories de g-modules. C. R. Acad. Sci. Paris Sér. I Math. 303 (1986), no. 15, 725-728. MR88c:17011
36. [St1] C. Stroppel, A generalization of Joseph's functor and shuffled Harish-Chandra bimodules. in preparation.
37. [St2] C. Stroppel, Categorification of the Temperley-Lieb category, Tangles and cobordisms via protective functors, Preprint Aarhus University (2003).
38. [St3] C. Stroppel, Category O: Gradings and Translation Functors. J. Algebra 268 (2003), no. 1, 301-326. MR2005290 (20041:17007)