Spherical analysis attached to some \(m\)-step nilpotent Lie group. (English) Zbl 07860407
Summary: We introduce a family of generalized Gelfand pairs \((K_m, N_m)\) where \(N_m\) is an \(m+2\)-step nilpotent Lie group and \(K_m\) 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 \(K_m\)-invariant and left invariant differential operators on \(N_m\).
MSC:
| 43A80 | Analysis on other specific Lie groups |
| 22E27 | Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) |
Software:
OEISReferences:
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