2006
DOI: 10.1155/ijmms/2006/48274
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Invariant triple products

Abstract: It is shown that the space of invariant trilinear forms on smooth representations of a semisimple Lie group is finite dimensional if the group is a product of hyperbolic groups. Explicit upper bounds are given which are attained in the case of induced representations. Applications to automorphic coefficients are given.

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Cited by 16 publications
(28 citation statements)
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“…As in the situations that were previously studied, the Bernstein-Reznikov integrals associated with spherical degenerate principal series of the complex symplectic group Sp(n, C) is can be expressed in terms of hypergeometric functions. The existence of the closed formula ( †) in the case n = 1 is consistent with the results obtained in the conformal case studied in [CKØP11], [CØ11] and [Dei06], in view of the isogeny between Sp(1, C) = SL(2, C) and SO • (3, 1).…”
Section: Closed Formulassupporting
confidence: 88%
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“…As in the situations that were previously studied, the Bernstein-Reznikov integrals associated with spherical degenerate principal series of the complex symplectic group Sp(n, C) is can be expressed in terms of hypergeometric functions. The existence of the closed formula ( †) in the case n = 1 is consistent with the results obtained in the conformal case studied in [CKØP11], [CØ11] and [Dei06], in view of the isogeny between Sp(1, C) = SL(2, C) and SO • (3, 1).…”
Section: Closed Formulassupporting
confidence: 88%
“…Such formulas have been obtained in the conformal case in [Dei06], [CØ11], [CKØP11] and [BKZ14] and further results were recently established by J.-L. Clerc in [Cle14,Cle15]. Similarly, closed formulas were found in the case of real symplectic groups in [CKØP11], where the methods used here find their origin.…”
Section: Closed Formulassupporting
confidence: 76%
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“…The crux of the proof is locally uniform comparison between L p and L ∞ norms of generalized matrix coefficients m v,η which is achieved by applying the model of [3] and [9] for the triple product functional η in spherical principal series.…”
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confidence: 99%