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On Asymptotic Behavior of Induced Representations

Published online by Cambridge University Press:  20 November 2018

Larry Baggett  and
Keith F. Taylor
Larry Baggett
Affiliation:
University of Colorado, Boulder, Colorado
Keith F. Taylor
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 1 , 01 February 1982 , pp. 220 - 232
Copyright
Copyright © Canadian Mathematical Society 1982

References

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