A Hadwiger-type theorem for the special unitary group

Details A Hadwiger-type theorem for the special unitary group A Hadwiger-type theorem for the special unitary group

2008-01-10

arxiv.org/abs/0801.1606v4

Geom. Funct. Anal. 19 (2009), 356-372

Mathematics

Differential Geometry

19 pages, minor changes, to appear in GAFA

Scientific paper

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