Duke Mathematical Journal

Characteristic cycles for the loop Grassmannian and nilpotent orbits

Sam Evens and Ivan Mirković

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Article information

Source
Duke Math. J., Volume 97, Number 1 (1999), 109-126.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077228504

Digital Object Identifier
doi:10.1215/S0012-7094-99-09705-3

Mathematical Reviews number (MathSciNet)
MR1682280

Zentralblatt MATH identifier
1160.22306

Subjects
Primary: 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05]
Secondary: 20G05: Representation theory 32C38: Sheaves of differential operators and their modules, D-modules [See also 14F10, 16S32, 35A27, 58J15]

Citation

Evens, Sam; Mirković, Ivan. Characteristic cycles for the loop Grassmannian and nilpotent orbits. Duke Math. J. 97 (1999), no. 1, 109--126. doi:10.1215/S0012-7094-99-09705-3. https://projecteuclid.org/euclid.dmj/1077228504


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References

  • [ABV] 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 Boston Inc., Boston, MA, 1992.
  • [BK] J. Bernstein and D. Kazhdan, An example of a non-rational variety $\hat{\mathcal{B}}_{N}$ for $G={\mathrm{Sp}}(6)$, appendix to D. Kazhdan and G. lusztig, Fixed point varieties on affine flag manifolds, Israel J. Math 62 (1988), 129–168.
  • [BoF] Brian D. Boe and Joseph H. G. Fu, Characteristic cycles in Hermitian symmetric spaces, Canad. J. Math. 49 (1997), no. 3, 417–467.
  • [BorM] Walter Borho and Robert MacPherson, Partial resolutions of nilpotent varieties, Analysis and topology on singular spaces, II, III (Luminy, 1981), Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 23–74.
  • [Br] T. Braden, Characteristic cycles of toric varieties; perverse sheaves on rank stratifications, Ph.D. thesis, Massachusetts Institute of Technology, 1995.
  • [BreFL] P. Bressler, M. Finkelberg, and V. Lunts, Vanishing cycles on Grassmannians, Duke Math. J. 61 (1990), no. 3, 763–777.
  • [Ca] Roger W. Carter, Finite groups of Lie type, Wiley Classics Library, John Wiley & Sons Ltd., Chichester, 1993, Conjugacy Classes and Complex Character.
  • [Du] Alberto S. Dubson, Classes caractéristiques des variétés singulières, C. R. Acad. Sci. Paris Sér. A-B 287 (1978), no. 4, A237–A240.
  • [EM] Sam Evens and Ivan Mirković, Fourier transform and the Iwahori-Matsumoto involution, Duke Math. J. 86 (1997), no. 3, 435–464.
  • [GG] H. Garland and I. Grojnowski, Affine Hecke algebras associated to Kac-Moody groups, preprint, q-alg 9508019.
  • [GeKZ] I. M. Gel'fand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Mathematics: Theory & Applications, Birkhäuser Boston Inc., Boston, MA, 1994.
  • [Gi1] V. Ginsburg, Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), no. 2, 327–402, Part 1.
  • [Gi2] Victor Ginzburg, Induction and restriction of character sheaves, I. M. Gel'fand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 149–167.
  • [Gi3] V. Ginzburg, Perverse sheaves on a loop group and Langlands' duality, alg-geom/9511007.
  • [Gr] M. Grinberg, Morse groups in symmetric spaces corresponding to the symmetric group, math. AG 9802091.
  • [Ha] Thomas C. Hales, Hyperelliptic curves and harmonic analysis (why harmonic analysis on reductive $p$-adic groups is not elementary), Representation theory and analysis on homogeneous spaces (New Brunswick, NJ, 1993), Contemp. Math., vol. 177, Amer. Math. Soc., Providence, RI, 1994, pp. 137–169.
  • [HK] R. Hotta and M. Kashiwara, The invariant holonomic system on a semisimple Lie algebra, Invent. Math. 75 (1984), no. 2, 327–358.
  • [Hs] Wu-yi Hsiang, Kogomologicheskaya teoriya topologicheskikh grupp preobrazovanii, “Mir”, Moscow, 1979, (in Russian).
  • [Ka1] Masaki Kashiwara, Systems of microdifferential equations, Progress in Mathematics, vol. 34, Birkhäuser Boston Inc., Boston, MA, 1983.
  • [Ka2] M. Kashiwara, The flag manifold of Kac-Moody Lie algebra, Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, MD, 1989, pp. 161–190.
  • [KaSa] Masaki Kashiwara and Yoshihisa Saito, Geometric construction of crystal bases, Duke Math. J. 89 (1997), no. 1, 9–36.
  • [KaSc] Masaki Kashiwara and Pierre Schapira, Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 292, Springer-Verlag, Berlin, 1990.
  • [KaT] Masaki Kashiwara and Toshiyuki Tanisaki, Kazhdan-Lusztig conjecture for affine Lie algebras with negative level, Duke Math. J. 77 (1995), no. 1, 21–62.
  • [La] Gérard Laumon, Correspondance de Langlands géométrique pour les corps de fonctions, Duke Math. J. 54 (1987), no. 2, 309–359.
  • [Le] Lê D ung Tráng, Limites d'espaces tangents et obstruction d'Euler des surfaces, The Euler-Poincaré characteristic (French), Astérisque, vol. 82, Soc. Math. France, Paris, 1981, pp. 45–69.
  • [Lu1] G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. in Math. 42 (1981), no. 2, 169–178.
  • [Lu2] George Lusztig, Singularities, character formulas, and a $q$-analog of weight multiplicities, Analysis and topology on singular spaces, II, III (Luminy, 1981), Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 208–229.
  • [Lu3] G. Lusztig, Intersection cohomology complexes on a reductive group, Invent. Math. 75 (1984), no. 2, 205–272.
  • [Lu4]1 George Lusztig, Character sheaves. I, Adv. in Math. 56 (1985), no. 3, 193–237.
  • [Lu4]2 George Lusztig, Character sheaves. II, Adv. in Math. 57 (1985), no. 3, 226–265.
  • [Lu4]3 George Lusztig, Character sheaves. III, Adv. in Math. 57 (1985), no. 3, 266–315.
  • [Lu4]4 George Lusztig, Character sheaves. IV, Adv. in Math. 59 (1986), no. 1, 1–63.
  • [Lu4]5 George Lusztig, Character sheaves. V, Adv. in Math. 61 (1986), no. 2, 103–155.
  • [M] I. Mirković, Character sheaves on reductive Lie algebras, preprint, 1988.
  • [MV1] I. Mirković and K. Vilonen, Characteristic varieties of character sheaves, Invent. Math. 93 (1988), no. 2, 405–418.
  • [MV2] I. Mirković and K. Vilonen, Perverse sheaves on loop Grassmannians and Langlands duality, alg. geom /9703010.
  • [Ro] W. Rossmann, Invariant eigendistributions on a semisimple Lie algebra and homology classes on the conormal variety. II. Representations of Weyl groups, J. Funct. Anal. 96 (1991), no. 1, 155–193.
  • [SV] W. Schmid and K. Vilonen, Weyl group actions on Lagrangian cycles and Rossmann's formula, Noncompact Lie groups and some of their applications (San Antonio, TX, 1993), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 429, Kluwer Acad. Publ., Dordrecht, 1994, pp. 243–250.
  • [S1] Peter Slodowy, Simple singularities and simple algebraic groups, Lecture Notes in Mathematics, vol. 815, Springer, Berlin, 1980.
  • [St] Robert Steinberg, Conjugacy classes in algebraic groups, Springer-Verlag, Berlin, 1974, Lecture Notes in Math., 366.
  • [Te] Bernard Teissier, Cycles évanescents, sections planes et conditions de Whitney, Singularités à Cargèse (Rencontre Singularités Géom. Anal., Inst. Études Sci., Cargèse, 1972), Soc. Math. France, Paris, 1973, 285–362. Astérisque, Nos. 7 et 8.