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Representation Theory

ISSN 1088-4165



Cohomology of classifying spaces and hermitian representations

Author: George Lusztig
Journal: Represent. Theory 1 (1997), 31-36
MSC (1991): Primary 20G99
Published electronically: November 4, 1996
MathSciNet review: 1429373
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Abstract: It is shown that a large part of the cohomology of the classifying space of a Lie group satisfying certain hypotheses can be obtained by a difference construction from hermitian representations of that Lie group. This result is relevant to the study of Novikov’s higher signatures.

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

  • A. Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. Math. 57 (1953), 115-207.
  • M. Gromov, Positive curvature, macroscopic dimension, spectral gaps and higher signatures, Functional analysis on the eve of the 21-st century, in honor of I. M. Gelfand, vol. II, Progr. in Math. 132, Birkhäuser, Boston, 1996.
  • G. Lusztig, Novikov’s higher signature and families of elliptic operators, J. Diff. Geom. 7 (1971), 225-256.

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Additional Information

George Lusztig
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID: 117100

Received by editor(s): August 13, 1996
Received by editor(s) in revised form: August 21, 1996
Published electronically: November 4, 1996
Additional Notes: Supported in part by the National Science Foundation
Article copyright: © Copyright 1997 American Mathematical Society