A Hadwiger-type theorem for the special unitary group

Abstract

The dimension of the space of SU(n) and translation invariant continuous valuations on ${\mathbb{C}}^n,n\ge 2$ 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.

19 pages, minor changes, to appear in GAFA

References in corpus (1)

• Valuations on convex sets, non-commutative determinants, and pluripotential theory