IMPORTANT NOTICE

The AMS website will be down for maintenance on May 23 between 6:00am - 8:00am EDT. For questions please contact AMS Customer Service at cust-serv@ams.org or (800) 321-4267 (U.S. & Canada), (401) 455-4000 (Worldwide).

 

Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The Chern character
for classical matrix groups


Author: Jay A. Wood
Journal: Proc. Amer. Math. Soc. 126 (1998), 1237-1244
MSC (1991): Primary 55R40
DOI: https://doi.org/10.1090/S0002-9939-98-04316-0
MathSciNet review: 1443417
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give explicit formulas for representations of classical matrix groups whose Chern characters have lowest order terms equal to standard characteristic classes. For $\operatorname{SO}(2r)$, the Euler class $e$ does not arise in this way, but $2^{r-1} e$ does arise in this way.


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

  • 1. J. F. Adams, On Chern characters and the structure of the unitary group, Proc. Camb. Phil. Soc. 57 (1961), 189-199. MR 22:12525
  • 2. M. F. Atiyah and F. Hirzebruch, Quelques théorèmes de non-plongement pour les variétés différentiables, Bull. Soc. Math. France 87 (1959), 383-396. MR 22:5055
  • 3. -, Vector bundles and homogeneous spaces, Differential Geometry, Proc. Symp. Pure Math., vol. 3, Amer. Math. Soc., Providence, RI, 1963, pp. 7-38. MR 25:2617
  • 4. A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538. MR 21:1586
  • 5. Th. Bröcker and T. tom Dieck, Representations of compact Lie groups, Grad. Texts Math., vol. 98, Springer-Verlag, New York, Berlin, Heidelberg, and Tokyo, 1985. MR 86i:22023
  • 6. D. Husemoller, Fibre bundles, 2nd ed., Grad. Texts Math., vol. 20, Springer-Verlag, New York, Heidelberg, and Berlin, 1975. MR 51:6805
  • 7. C. R. F. Maunder, Chern characters and higher order cohomology operations, Proc. Camb. Phil. Soc. 60 (1964), 751-764. MR 31:2722

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 55R40

Retrieve articles in all journals with MSC (1991): 55R40


Additional Information

Jay A. Wood
Affiliation: Department of Mathematics, Computer Science & Statistics, Purdue University Calumet, Hammond, Indiana 46323-2094
Email: wood@calumet.purdue.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04316-0
Received by editor(s): October 1, 1996
Additional Notes: The author was partially supported by NSA grants MDA904-94-H-2025 and MDA904-96-1-0067, and by Purdue University Calumet Scholarly Research Awards.
Dedicated: To S. S. Chern
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society