Geometric and Functional Analysis

, Volume 19, Issue 2, pp 356-372

First online:

A Hadwiger-Type Theorem for the Special Unitary Group

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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.

Keywords and phrases

Valuation kinematic formula integral geometry

2000 Mathematics Subject Classification

53C65 52A22