0000000000226458
AUTHOR
Amel Zergane
showing 2 related works from this author
Separation of representations with quadratic overgroups
2011
AbstractAny unitary irreducible representation π of a Lie group G defines a moment set Iπ, subset of the dual g⁎ of the Lie algebra of G. Unfortunately, Iπ does not characterize π. If G is exponential, there exists an overgroup G+ of G, built using real-analytic functions on g⁎, and extensions π+ of any generic representation π to G+ such that Iπ+ characterizes π.In this paper, we prove that, for many different classes of group G, G admits a quadratic overgroup: such an overgroup is built with the only use of linear and quadratic functions.
Erratum to “Separation of representations with quadratic overgroups” [Bull. Sci. Math. 135 (2) (2011) 141–165]
2011
Abstract In the paper entitled “Separation of representations with quadratic overgroups”, we defined the notion of quadratic overgroups, and announced that the 6-dimensional nilpotent Lie algebra g 6 , 20 admits such a quadratic overgroup. There is a mistake in the proof. The present Erratum explains that the proposed overgroup is only weakly quadratic, and g 6 , 20 does not admit any natural quadratic overgroup.