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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.

References [Enhancements On Off] (What's this?)

  • [B] J.-P. Brasselet, Existence des classes de Chern en théorie bivariante, Astérisque 101-102 (1981), 7-22. MR 85j:32019
  • [CG] N. Chriss and V. Ginzburg, Representation theory and complex geometry, Birkhäuser, 1997. MR 98i:22021
  • [F] W. Fulton, Intersection Theory, Springer-Verlag, 1984. MR 85k:14004
  • [FM] W. Fulton and R. MacPherson, Categorical frameworks for the study of singular spaces, Memoirs of Amer. Math. Soc. 31 (1981). MR 83a:55015
  • [G1] V. Ginzburg, $\mathfrak{G}$-Modules, Springer's Representations and Bivariant Chern Classes, Adv. in Maths. 61 (1986), 1-48. MR 87k:17014
  • [G2] -, Geometric methods in the representation theory of Hecke algebras and quantum groups, in ``Representation theories and algebraic geometry (Montreal, PQ, 1997)" (ed. by A. Broer and A. Daigneault), Kluwer Acad. Publ., Dordrecht, 1998, pp. 127-183. MR 99j:17020
  • [K] M. Kwiecinski, Formule du produit pour les classes caractéristiques de Chern-Schwartz-MacPherson et homologie d'intersection, C. R. Acad. Sci. Paris 314 (1992), 625-628. MR 93b:55008
  • [KY] M. Kwiecinski and S. Yokura, Product formula of the twisted MacPherson class, Proc. Japan Acad 68 (1992), 167-171. MR 94d:32052
  • [M] R. MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. 100 (1974), 423-432. MR 50:13587
  • [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

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

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