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.

中文翻译：

---

附加到三步幂等李群的广义Gelfand对

让Ñ是幂零李群和ķ自同构组的一子组紧凑AUT（Ñ的）ñ。众所周知，如果\（（K <imes N，K）\）是一个Gelfand对，则N最多为两步幂立李群。当K是一个非紧致基团时，将Gelfand对的概念推广。在这项工作中，我们给3步幂零李群和非紧凑子组的示例ķ的AUT（Ñ使得）\（（K <输入法编辑器N，N）\）是广义的Gelfand对。