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Invariant valuations on quaternionic vector spaces

Part of: Global differential geometry

Published online by Cambridge University Press:  24 January 2012

Andreas Bernig
Andreas Bernig
Affiliation:
Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Strasse 10, 60054 Frankfurt, Germany (bernig@math.uni-frankfurt.de)
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Abstract

The spaces of Sp(n)-, Sp(n) · U(1)- and Sp(n) · Sp(1)-invariant, translation-invariant, continuous convex valuations on the quaternionic vector space ℍn are studied. Combinatorial dimension formulae involving Young diagrams and Schur polynomials are proved.

Keywords

valuationsalgebraic integral geometryHadwiger's theoremcompact symplectic group

MSC classification

Secondary: 53C65: Integral geometry
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 3 , July 2012 , pp. 467 - 499
Copyright
Copyright © Cambridge University Press 2012

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