Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II: Taylor expansions on singular sets

Véronique Fischer; Fulvio Ricci; Oksana Yakimova

doi:10.1007/978-1-4614-7193-6_5

Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II: Taylor expansions on singular sets

Véronique Fischer, Fulvio Ricci, Oksana Yakimova

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

3 Citations (SciVal)

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 Σ_D, appropriately 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 Vinberg's condition. This means that the Lie algebra n of N (which is step 2) decomposes as v ⊕ [n,n] with v irreducible under K.

Original language	English
Title of host publication	Lie Groups
Subtitle of host publication	Structure, Actions, and Representations: In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday
Editors	A. Huckleberry, I. Penkov, G. Zuckerman
Place of Publication	New York, U. S. A.
Publisher	Birkhauser Boston
Pages	81-112
Number of pages	32
ISBN (Electronic)	9781461471936
ISBN (Print)	9781461471929
DOIs	https://doi.org/10.1007/978-1-4614-7193-6_5
Publication status	Published - 1 Jan 2013

Publication series

Name	Progress in Mathematics
Volume	306

Keywords

Gelfand pairs
Invariants
Schwartz functions
Spherical transform

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-1-4614-7193-6_5

Cite this

Fischer, V., Ricci, F., & Yakimova, O. (2013). Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II: Taylor expansions on singular sets. In A. Huckleberry, I. Penkov, & G. Zuckerman (Eds.), Lie Groups: Structure, Actions, and Representations: In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday (pp. 81-112). (Progress in Mathematics; Vol. 306). Birkhauser Boston. https://doi.org/10.1007/978-1-4614-7193-6_5

Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II: Taylor expansions on singular sets. / Fischer, Véronique; Ricci, Fulvio; Yakimova, Oksana.
Lie Groups: Structure, Actions, and Representations: In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday. ed. / A. Huckleberry; I. Penkov; G. Zuckerman. New York, U. S. A.: Birkhauser Boston, 2013. p. 81-112 (Progress in Mathematics; Vol. 306).

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

Fischer, V, Ricci, F & Yakimova, O 2013, Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II: Taylor expansions on singular sets. in A Huckleberry, I Penkov & G Zuckerman (eds), Lie Groups: Structure, Actions, and Representations: In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday. Progress in Mathematics, vol. 306, Birkhauser Boston, New York, U. S. A., pp. 81-112. https://doi.org/10.1007/978-1-4614-7193-6_5

Fischer V, Ricci F, Yakimova O. Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II: Taylor expansions on singular sets. In Huckleberry A, Penkov I, Zuckerman G, editors, Lie Groups: Structure, Actions, and Representations: In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday. New York, U. S. A.: Birkhauser Boston. 2013. p. 81-112. (Progress in Mathematics). doi: 10.1007/978-1-4614-7193-6_5

Fischer, Véronique ; Ricci, Fulvio ; Yakimova, Oksana. / Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II : Taylor expansions on singular sets. Lie Groups: Structure, Actions, and Representations: In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday. editor / A. Huckleberry ; I. Penkov ; G. Zuckerman. New York, U. S. A. : Birkhauser Boston, 2013. pp. 81-112 (Progress in Mathematics).

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Nilpotent Gelfand pairs and spherical transforms of Schwartz functions II: Taylor expansions on singular sets

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