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Cohomology of classifying spaces and hermitian representations

Author(s): George Lusztig
Journal: Represent. Theory 1 (1997), 31 - 36.
MSC (1991): Primary 20G99
Posted: November 4, 1996
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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:

[B]: A. Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. Math. 57 (1953), 115-207. MR 14:490e
[G]: 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. CMP 96:12
[L]: G. Lusztig, Novikov's higher signature and families of elliptic operators, J. Diff. Geom. 7 (1971), 225-256.


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