6533b7d4fe1ef96bd12620a6

RESEARCH PRODUCT

Separation of representations with quadratic overgroups

Amel ZerganeMohamed SelmiDidier Arnal

subject

Pure mathematicsMathematics(all)Group (mathematics)General MathematicsQuadratic overgroupLie groupQuadratic functionGroup representationAlgebraUnitary representationIrreducible representationLie algebraMoment mapLie groups representationsMoment mapMathematics

description

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.

yearjournalcountryeditionlanguage
2011-03-01Bulletin des Sciences Mathématiques
10.1016/j.bulsci.2010.12.001http://dx.doi.org/10.1016/j.bulsci.2010.12.001