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Journal of Lie Theory 13 (2003), No. 1, 077--089
Copyright Heldermann Verlag 2003

Lattices and Harmonic Analysis on Some 2-Step Solvable Lie Groups

Huale Huang
AT&T Labs-Research, 180 Park Avenue, Florham Park, NJ 07932, U.S.A.

This paper deals with a class of 2-step solvable simply connected Lie groups G in which we construct certain lattices  G.  It turns out that these are all the lattices in such groups. We then apply our results to study the decomposition of the quasi-regular representation of  G  on G / G.

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