Abstract
The dimension of the space of SU(n) and translation-invariant continuous valuations on \({\mathbb {C}^n}\), n ≥ 2, is computed. For even n, this dimension equals (n 2 + 3n + 10)/2; for odd n it equals (n 2 + 3n + 6)/2. An explicit geometric basis of this space is constructed. The kinematic formulas for SU(n) are obtained as corollaries.
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Supported by the Schweizerischer Nationalfonds grants SNF PP002-114715/1 and 200020-121506.
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Bernig, A. A Hadwiger-Type Theorem for the Special Unitary Group. Geom. Funct. Anal. 19, 356–372 (2009). https://doi.org/10.1007/s00039-009-0008-4
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DOI: https://doi.org/10.1007/s00039-009-0008-4