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The Wehrl entropy conjecture for coherent (highest weight) states inrepresentations of the Heisenberg group, which was proved in 1978 and recentlyextended by us to the group $SU(2)$, is further extended here to symmetricrepresentations of the groups $SU(N)$ for all $N$. This result gives furtherevidence for our conjecture that highest weight states minimize group integralsof certain concave functions for a large class of Lie groups and theirrepresentations.

Proof of the Wehrl-type Entropy Conjecture for Symmmetric SU(N) Coherent States