Proceedings of the American Mathematical Society

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Remarks on Ginzburg's bivariant Chern classes


Author: Shoji Yokura
Journal: Proc. Amer. Math. Soc. 130 (2002), 3465-3471
MSC (1991): Primary 14C17, 14F99, 55N35
Published electronically: March 29, 2002
MathSciNet review: 1918822
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Abstract: The convolution product is an important tool in the geometric representation theory. Ginzburg constructed the bivariant Chern class operation from a certain convolution algebra of Lagrangian cycles to the convolution algebra of Borel-Moore homology. In this paper we give some remarks on the Ginzburg bivariant Chern classes.


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  • [B] Jean-Paul Brasselet, Existence des classes de Chern en théorie bivariante, Analysis and topology on singular spaces, II, III (Luminy, 1981) Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 7–22 (French). MR 737926
  • [CG] Neil Chriss and Victor Ginzburg, Representation theory and complex geometry, Birkhäuser Boston, Inc., Boston, MA, 1997. MR 1433132
  • [F] William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620
  • [FM] William Fulton and Robert MacPherson, Categorical framework for the study of singular spaces, Mem. Amer. Math. Soc. 31 (1981), no. 243, vi+165. MR 609831, 10.1090/memo/0243
  • [G1] V. Ginsburg, 𝔊-modules, Springer’s representations and bivariant Chern classes, Adv. in Math. 61 (1986), no. 1, 1–48. MR 847727, 10.1016/0001-8708(86)90064-2
  • [G2] Victor Ginzburg, Geometric methods in the representation theory of Hecke algebras and quantum groups, Representation theories and algebraic geometry (Montreal, PQ, 1997), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 514, Kluwer Acad. Publ., Dordrecht, 1998, pp. 127–183. Notes by Vladimir Baranovsky [V. Yu. Baranovskiĭ]. MR 1649626
  • [K] Michał Kwieciński, Formule du produit pour les classes caractéristiques de Chern-Schwartz-MacPherson et homologie d’intersection, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), no. 8, 625–628 (French, with English summary). MR 1158750
  • [KY] Michał Kwieciński and Shoji Yokura, Product formula for twisted MacPherson classes, Proc. Japan Acad. Ser. A Math. Sci. 68 (1992), no. 7, 167–171. MR 1193174
  • [M] R. D. MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. (2) 100 (1974), 423–432. MR 0361141
  • [N1] H. Nakajima, Quiver varieties and quantum affine algebras (in Japanese), Suugaku 52 (2000), 337-359. CMP 2001:06
  • [N2] -, Quiver varieties and finite dimensional representations of quantum affine algebras, J. Amer. Math. Soc. 14 (2001), 145-238. CMP 2001:07
  • [Y1] S. Yokura, On the uniqueness problem of the bivariant Chern classes, preprint (2001).
  • [Y2] -, On Ginzburg's bivariant Chern classes, preprint (2001).
  • [Y3] -, On Ginzburg's bivariant Chern classes, II, preprint (2001).

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Additional Information

Shoji Yokura
Affiliation: Department of Mathematics and Computer Science, Faculty of Science, University of Kagoshima, 21-35 Korimoto 1-chome, Kagoshima 890-0065, Japan
Email: yokura@sci.kagoshima-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06489-4
Keywords: Bivariant theory, Chern-Schwartz-MacPherson class, constructible function, convolution
Received by editor(s): May 25, 2001
Received by editor(s) in revised form: July 6, 2001
Published electronically: March 29, 2002
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (C) (No.12640081), the Japanese Ministry of Education, Science, Sports and Culture.
Communicated by: Paul Goerss
Article copyright: © Copyright 2002 American Mathematical Society