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Displaying similar documents to “The Schwartz space of a general semisimple Lie group. IV : elementary mixed wave packets”

The duality correspondence of infinitesimal characters

Tomasz Przebinda (1996)

Colloquium Mathematicae

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We determine the correspondence of infinitesimal characters of representations which occur in Howe's Duality Theorem. In the appendix we identify the lowest K-types, in the sense of Vogan, of the unitary highest weight representations of real reductive dual pairs with at least one member compact.

Globality in semisimple Lie groups

Karl-Hermann Neeb (1990)

Annales de l'institut Fourier

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In the first section of this paper we give a characterization of those closed convex cones (wedges) W in the Lie algebra s l ( 2 , R ) n which are invariant under the maximal compact subgroup of the adjoint group and which are controllable in the associated simply connected Lie group S l ( 2 , R ) n , i.e., for which the subsemigroup S = ( exp W ) generated by the exponential image of W agrees with the whole group G (Theorem 13). In Section 2 we develop some algebraic tools concerning real root decompositions with respect to...