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Commuting elements in central products of special unitary groups

Part of: Linear algebraic groups and related topics Fiber spaces and bundles

Published online by Cambridge University Press:  24 October 2012

Alejandro Adem ,
F. R. Cohen  and
José Manuel Gómez
Alejandro Adem
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada (adem@math.ubc.ca)
F. R. Cohen
Affiliation:
Department of Mathematics, University of Rochester, Rochester, NY 14627, USA (cohf@math.rochester.edu)
José Manuel Gómez
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada (adem@math.ubc.ca)
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Abstract

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We study the space of commuting elements in the central product Gm,p of m copies of the special unitary group SU(p), where p is a prime number. In particular, a computation for the number of path-connected components of these spaces is given and the geometry of the moduli space Rep(ℤn, Gm,p) of isomorphism classes of flat connections on principal Gm,p-bundles over the n-torus is completely described for all values of n, m and p.

Keywords

commuting elementsLie groups

MSC classification

Secondary: 55R40: Homology of classifying spaces, characteristic classes 20G05: Representation theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 1 - 12
Copyright
Copyright © Edinburgh Mathematical Society 2012

References

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