Abstract
Let N be a nilpotent Lie group and K a compact subgroup of the automorphism group Aut(N) of N. It is well-known that if \((K < imes N,K)\) is a Gelfand pair then N is at most 2-step nilpotent Lie group. The notion of Gelfand pair was generalized when K is a non-compact group. In this work, we give an example of a 3-step nilpotent Lie group and a non-compact subgroup K of Aut(N) such that \((K < imes N,N)\) is a generalized Gelfand pair.
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We are grateful to G. Ratcliff who let us know the article [9].
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Communicated by Fulvio Ricci.
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Gallo, A.L., Saal, L.V. A Generalized Gelfand Pair Attached to a 3-Step Nilpotent Lie Group. J Fourier Anal Appl 26, 62 (2020). https://doi.org/10.1007/s00041-020-09772-4
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DOI: https://doi.org/10.1007/s00041-020-09772-4