Vol. 306, No. 2, 2020

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Isotypic multiharmonic polynomials and Gelbart–Helgason reciprocity

Anthony C. Kable

Vol. 306 (2020), No. 2, 519–538
Abstract

A result of Gelbart and Helgason that describes the harmonic analysis of the space of functions on certain Stiefel manifolds and a result of Folland that describes the harmonic analysis of the de Rham complex on a sphere are generalized to describe the harmonic analysis of the de Rham complex on certain Stiefel manifolds. Equivalently, the cobranching law from a fundamental representation of an orthogonal group to a larger orthogonal group is determined.

Keywords
representation, orthogonal group, general linear group, branching law, cobranching law
Mathematical Subject Classification 2010
Primary: 20G05
Milestones
Received: 12 July 2019
Revised: 5 January 2020
Accepted: 8 January 2020
Published: 13 July 2020
Authors
Anthony C. Kable
Department of Mathematics
Oklahoma State University
Stillwater, OK
United States