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Mosc. Math. J., 2004, Volume 4, Number 1, Pages 153–179 (Mi mmj146)  

This article is cited in 32 scientific papers (total in 32 papers)

Parabolic character sheaves. I

G. Lusztig

Department of Mathematics, Massachusetts Institute of Technology

Abstract: We study a class of perverse sheaves on the variety of pairs $(P,gUP)$ where $P$ runs through a conjugacy class of parabolics in a connected reductive group and $gUP$ runs through $G/UP$. This is a generalization of the theory of character sheaves.

Key words and phrases: Reductive group, parabolic group, perverse sheaf, character sheaf.

DOI: https://doi.org/10.17323/1609-4514-2004-4-1-153-179

Full text: http://www.ams.org/.../abst4-1-2004.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 20G99
Received: February 26, 2003
Language:

Citation: G. Lusztig, “Parabolic character sheaves. I”, Mosc. Math. J., 4:1 (2004), 153–179

Citation in format AMSBIB
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\by G.~Lusztig
\paper Parabolic character sheaves.~I
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 1
\pages 153--179
\mathnet{http://mi.mathnet.ru/mmj146}
\crossref{https://doi.org/10.17323/1609-4514-2004-4-1-153-179}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2074987}
\zmath{https://zbmath.org/?q=an:1102.20030}
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    This publication is cited in the following articles:
    1. G. Lusztig, “Parabolic character sheaves. II”, Mosc. Math. J., 4:4 (2004), 869–896  mathnet  mathscinet  zmath
    2. He Xuhua, “The character sheaves on the group compactification”, Adv. Math., 207:2 (2006), 805–827  crossref  mathscinet  zmath  isi  scopus
    3. Evens S., Lu Jiang-Hua, “On the variety of Lagrangian subalgebras. II”, Ann. Sci. Icole Norm. Sup. (4), 39:2 (2006), 347–379  crossref  mathscinet  zmath  isi  scopus
    4. He Xuhua, “Unipotent variety in the group compactification”, Adv. Math., 203:1 (2006), 109–131  crossref  mathscinet  zmath  isi
    5. Lusztig G., “Character sheaves and generalizations”, Unity of Mathematics - IN HONOR OF THE NINETIETH BIRTHDAY OF I.M. GELFAND, Progress in Mathematics, 244, 2006, 443–455  crossref  mathscinet  zmath  isi  scopus
    6. Lu J.-H., Yakimov M., “Partitions of the wonderful group compactification”, Transformation Groups, 12:4 (2007), 695–723  crossref  mathscinet  zmath  isi  scopus
    7. He X., “Minimal length elements in some double cosets of Coxeter groups”, Advances in Mathematics, 215:2 (2007), 469–503  crossref  mathscinet  zmath  isi  scopus
    8. Springer T.A., “An extension of Bruhat's lemma”, Journal of Algebra, 313:1 (2007), 417–427  crossref  mathscinet  zmath  isi  scopus
    9. He X., “The G-stable pieces of the wonderful compactification”, Transactions of the American Mathematical Society, 359:7 (2007), 3005–3024  crossref  mathscinet  zmath  isi  scopus
    10. Lu J.-H., Yakimov M., “Group orbits and regular partitions of Poisson manifolds”, Communications in Mathematical Physics, 283:3 (2008), 729–748  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. He X., Lusztig G., “Singular supports for character sheaves on a group compactification”, Geometric and Functional Analysis, 17:6 (2008), 1915–1923  crossref  mathscinet  zmath  isi  scopus
    12. He X., “Character sheaves on certain spherical varieties”, Advances in Mathematics, 217:3 (2008), 1154–1191  crossref  mathscinet  zmath  isi  scopus
    13. G. Lusztig, “Notes on character sheaves”, Mosc. Math. J., 9:1 (2009), 91–109  mathnet  mathscinet  zmath
    14. He X., “G-stable pieces and partial flag varieties”, Representation Theory-Bk, Contemporary Mathematics, 478, 2009, 61–70  crossref  mathscinet  zmath  isi
    15. Hoeve M., “Ekedahl-Oort strata in the supersingular locus”, Journal of the London Mathematical Society-Second Series, 81:1 (2010), 129–141  crossref  mathscinet  zmath  isi  scopus
    16. G. Lusztig, “Parabolic Character Sheaves, III”, Mosc. Math. J., 10:3 (2010), 603–609  mathnet  mathscinet
    17. He X., “Character sheaves on the semi-stable locus of a group compactification”, Adv Math, 225:6 (2010), 3258–3290  crossref  mathscinet  zmath  isi  scopus
    18. Vasiu A., “Mod p classification of Shimura F-crystals”, Math Nachr, 283:8 (2010), 1068–1113  crossref  mathscinet  zmath  isi  scopus
    19. He X., Lu J.-H., “On Intersections of Certain Partitions of a Group Compactification”, Int Math Res Not, 2011, no. 11, 2534–2564  mathscinet  zmath  isi
    20. Springer T.A., “Remarks on Parabolic Character Sheaves”, Pure Appl Math Q, 7:4 (2011), 969–994  crossref  mathscinet  zmath  isi
    21. Springer T.A., “Decompositions related to symmetric varieties”, J Algebra, 329:1 (2011), 260–273  crossref  mathscinet  zmath  isi  scopus
    22. He X., “Closure of Steinberg Fibers and Affine Deligne-Lusztig Varieties”, Int Math Res Not, 2011, no. 14, 3237–3260  mathscinet  zmath  isi
    23. Goertz U., Hoeve M., “Ekedahl-Oort strata and Kottwitz-Rapoport strata”, J Algebra, 351:1 (2012), 160–174  crossref  mathscinet  zmath  isi  scopus
    24. Esposito F., “Closures of Orbits Under the Diagonal Action in the Wonderful Compactification of Pgl(3)”, Commun. Algebr., 40:8 (2012), 3127–3140  crossref  mathscinet  zmath  isi  scopus
    25. Viehmann E., “Truncations of Level 1 of Elements in the Loop Group of a Reductive Group”, Ann. Math., 179:3 (2014), 1009–1040  crossref  mathscinet  zmath  isi  scopus
    26. Bouthier A., “Dimension Des Fibres de Springer Affines Pour Les Groupes”, Transform. Groups, 20:3 (2015), 615–663  crossref  mathscinet  zmath  isi  elib  scopus
    27. He X., Nie S., “P-Alcoves, Parabolic Subalgebras and Cocenters of Affine Hecke Algebras”, Sel. Math.-New Ser., 21:3 (2015), 995–1019  crossref  mathscinet  zmath  isi  scopus
    28. Pink R., Wedhorn T., Ziegler P., “F-Zips With Additional Structure”, Pac. J. Math., 274:1 (2015), 183–236  crossref  mathscinet  zmath  isi  scopus
    29. He X., Lam T., “Projected Richardson Varieties and Affine Schubert Varieties”, Ann. Inst. Fourier, 65:6 (2015), 2385–2412  crossref  mathscinet  zmath  isi
    30. Goertz U. He X., “Basic Loci of Coxeter Type in Shimura Varieties”, Camb. J. Math., 3:3 (2015), 323–353  crossref  mathscinet  zmath  isi
    31. Lusztig G., “Nonsplit Hecke Algebras and Perverse Sheaves”, Sel. Math.-New Ser., 22:4, SI (2016), 1953–1986  crossref  mathscinet  zmath  isi  scopus
    32. He X. Rapoport M., “Stratifications in the Reduction of Shimura Varieties”, Manuscr. Math., 152:3-4 (2017), 317–343  crossref  mathscinet  zmath  isi  scopus
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