Geometric and Functional Analysis

, Volume 19, Issue 2, pp 356–372

A Hadwiger-Type Theorem for the Special Unitary Group



DOI: 10.1007/s00039-009-0008-4

Cite this article as:
Bernig, A. Geom. Funct. Anal. (2009) 19: 356. doi:10.1007/s00039-009-0008-4


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 (n2 + 3n + 10)/2; for odd n it equals (n2 + 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

Valuationkinematic formulaintegral geometry

2000 Mathematics Subject Classification

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© Birkhäuser Verlag Basel/Switzerland 2009