\(H\)-type groups and Iwasawa decompositions
The authors study a class of nilpotent Lie groups known as groups of Heisenberg type (or \(H\)-type groups). The subgroups \(N\) in the Iwasawa decompositions of real rank one simple Lie groups are of \(H\)-type. The authors give a simple Lie-algebraic condition which distinguishes such Iwasawa \(N\)-groups among all \(H\)-type groups. Then they discuss various problems in the geometry of \(H\)-type groups which are inspired by the known results about Iwasawa \(N\)-groups used in harmonic analysis.
scientific article; zbMATH DE number 10142
scientific article