Spherical Analysis Attached to Some m-Step Nilpotent Lie Group

期刊论文
发表日期：

2024年4月2日

查看全文

Silvina Campos,
José García,
Linda Saal

摘要

We introduce a family of generalized Gelfand pairs $(K_m,N_m)$ $(K_{m}, N_{m})$ where $N_m$ $N_{m}$ is an $m+2$ $m + 2$ -step nilpotent Lie group and $K_m$ $K_{m}$ is isomorphic to the 3-dimensional Heisenberg group. We develop the associated spherical analysis computing the set of the spherical distributions and we obtain some results on the algebra of $K_m$ $K_{m}$ -invariant and left invariant differential operators on $N_m$ $N_{m}$ .