The Plancherel formula for the horocycle spaces and generalizations, II

Journal of the Australian Mathematical Society

Ronald L. Lipsman¹ 

关键词: primary 22E46;    secondary 22E45;   

DOI  :  10.1017/S1446788700034959

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

The Plancherel formula for various semisimple homogeneous spaces with non-reductive stability group is derived within the framework of the Bonnet Plancherel formula for the direct integral decomposition of a quasi-regular representation. These formulas represent a continuation of the author's program to establish a new paradigm for concrete Plancherel analysis on homogeneous spaces wherein the distinction between finite and infinite multiplicity is de-emphasized. One interesting feature of the paper is the computation of the Bonnet nuclear operators corresponding to certain exponential representations (roughly those induced from infinite-dimensional representations of a subgroup). Another feature is a natural realization of the direct integral decomposition over a canonical set of concrete irreducible representations, rather than over the unitary dual.

【 授权许可】

Unknown