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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