Spaces of bounded spherical functions on Heisenberg groups: part II

作者：Benson Chal^*; Ratcliff Gail

来源：Annali di Matematica Pura ed Applicata, 2015, 194(2): 533-561.

DOI：10.1007/s10231-013-0387-x

• Gelfand pairs
• Spherical functions
• Nilpotent Lie groups
• Orbit method

Consider a linear multiplicity free action by a compact Lie group K on a finite dimensional Hermitian vector space V. Letting K act on the Heisenberg group H-V = V x R yields a Gelfand pair. The condition that K : V be "well-behaved" establishes a relationship between the associated moment mapping and highest weight vectors occurring in the polynomial ring C[V]. Under this condition, an application of the Orbit Method produces a topological embedding of the space of bounded spherical functions for (K, H-V) in the space of K-orbits in the dual of the Lie algebra for H-V. In part I of this work, it was shown that every irreducible multiplicity free action is well-behaved. Here we extend this result to encompass all multiplicity free actions. Our proof uses case-by-case analysis of multiplicity free actions which are indecomposable but not irreducible.

• 出版日期2015-4