A family of generalized Gelfand pairs attached to $3$-step nilpotent Lie groups

Mai Katada, Cornelie Mitcha Malanda

It is well known that if $(K⋉N,K)$ is a Gelfand pair with $N$ a nilpotent Lie group and $K$ a compact subgroup of the automorphism group of $N$, then $N$ is at most $2$-ste…