Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II. Taylor expansion on singular sets
File(s)
Working paper
Author(s)
Fischer, V
Ricci, F
Yakimova, O
Type
Report
Abstract
This paper is a continuation of [8], in the direction of proving the conjecture that the spherical transform on a nilpotent Gelfand pair (N,K) establishes an isomorphism between the space of K-invariant Schwartz functions on N and the space of Schwartz functions restricted to the Gelfand spectrum properly embedded in a Euclidean space. We prove a result, of independent interest for the representation theoretical problems that are involved, which can be viewed as a generalised Hadamard lemma for K-invariant functions on N. The context is that of nilpotent Gelfand pairs satisfying Vinbergs condition. This means that the Lie algebra n of N (which is step 2) decomposes as a direct sum of [n,n] and a K-invariant irreducible subspace.
Date Issued
2014-05-15
Copyright Statement
© 2011 The Authors
Description
15.05.14 KB Ok to add to working paper to spiral, author retains copyright
Identifier
http://arxiv.org/abs/1008.4699v2
Notes
Second version has an improved introduction