Illinois Journal of Mathematics

Compact actions, retract theory and prime ideals

Raza Lahiani and Carine Molitor-Braun

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Let $N$ be a connected, simply connected, nilpotent Lie group and let $K$ be a compact subgroup of the automorphism group of $N$. We study the density of Schwartz functions in the kernels of $K$-orbits and characterize $K$-prime ideals. For this purpose a retract theory for $K$-actions has to be established.

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Illinois J. Math., Volume 55, Number 3 (2011), 1235-1266.

First available in Project Euclid: 29 May 2013

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Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX] 22E27: Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) 43A20: $L^1$-algebras on groups, semigroups, etc.


Lahiani, Raza; Molitor-Braun, Carine. Compact actions, retract theory and prime ideals. Illinois J. Math. 55 (2011), no. 3, 1235--1266. doi:10.1215/ijm/1369841804.

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