Characteristically nilpotent Lie groups with flat coadjoint orbits

2024/08/20 by Burde, Dietrich, van Velthoven, Jordy Timo · 1 citation
#17A36 #17B30 #22E27 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2408.10660

Abstract

We study the existence of certain characteristically nilpotent Lie algebras with flat coadjoint orbits. Their connected, simply connected Lie groups admit square-integrable representations modulo the center. There are many examples of nilpotent Lie groups admitting families of dilations and square-integrable representations. Much less is known about examples admitting square-integrable representations for which the quotient by the center does not admit a family of dilations. In this paper we construct a two-parameter family of characteristically nilpotent Lie groups G(α,β) in dimension 11, admitting square-integrable representations modulo the center Z, such that G(α,β)/Z does not admit a family of dilations.

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