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The Chern character for classical matrix groups
Author(s):
Jay
A.
Wood
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1237-1244.
MSC (1991):
Primary 55R40
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Abstract:
We give explicit formulas for representations of classical matrix groups whose Chern characters have lowest order terms equal to standard characteristic classes. For  , the Euler class  does not arise in this way, but  does arise in this way.
References:
- 1.
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- 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
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- -, 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
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- A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538. MR 21:1586
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- 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
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- D. Husemoller, Fibre bundles, 2nd ed., Grad. Texts Math., vol. 20, Springer-Verlag, New York, Heidelberg, and Berlin, 1975. MR 51:6805
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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:
10.1090/S0002-9939-98-04316-0
PII:
S 0002-9939(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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