Geodesic
On Asymptotic Behavior of Induced Representations
Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 220-232

Voir la notice de l'article provenant de la source Cambridge University Press

This paper is devoted to the proof of the following theorem.THEOREM 1.1. Let H be a closed subgroup of a connected Lie group G, let N denote the largest (closed) subgroup of H which is normal in all of G, and suppose that π is a unitary representation of H whose restriction to N is a multiple of a character χ of N. Then every matrix coefficient of the induced representation Uπ vanishes at infinity modulo the kernel of Uπ providing that the following two conditions hold: i) N is almost-connected (finite modulo its connected component). ii) The subgroup Hk is “regularly related” to the diagonal subgroup D in Gk for at least one integer k ≧ k0 where k0 is determined by G and H. 
Baggett, Larry; Taylor, Keith F. On Asymptotic Behavior of Induced Representations. Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 220-232. doi: 10.4153/CJM-1982-015-8
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