Previous |  Up |  Next


Title: Spectrum generating on twistor bundle (English)
Author: Branson, Thomas
Author: Hong, Doojin
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 42
Issue: 5
Year: 2006
Pages: 169-183
Summary lang: English
Category: math
Summary: Spectrum generating technique introduced by Ólafsson, Ørsted, and one of the authors in the paper (Branson, T., Ólafsson, G. and Ørsted, B., Spectrum generating operators, and intertwining operators for representations induced from a maximal parabolic subgroups, J. Funct. Anal. 135 (1996), 163–205.) provides an efficient way to construct certain intertwinors when $K$-types are of multiplicity at most one. Intertwinors on the twistor bundle over $S^1\times S^{n-1}$ have some $K$-types of multiplicity 2. With some additional calculation along with the spectrum generating technique, we give explicit formulas for these intertwinors of all orders. (English)
MSC: 22E46
MSC: 53C28
idZBL: Zbl 1164.53358
idMR: MR2322405
Date available: 2008-06-06T22:49:20Z
Last updated: 2012-05-10
Stable URL:
Reference: [1] Branson T.: Group representations arising from Lorentz conformal geometry.J. Funct. Anal. 74 (1987), 199–291. Zbl 0643.58036, MR 0904819
Reference: [2] Branson T.: Nonlinear phenomena in the spectral theory of geometric linear differential operators.Proc. Symp. Pure Math. 59 (1996), 27–65. Zbl 0857.58042, MR 1392983
Reference: [3] Branson T.: Stein-Weiss operators and ellipticity.J. Funct. Anal. 151 (1997), 334–383. Zbl 0904.58054, MR 1491546
Reference: [4] Branson T.: Spectra of self-gradients on spheres.J. Lie Theory 9 (1999), 491–506. Zbl 1012.22026, MR 1718236
Reference: [5] Branson T., Ólafsson G., Ørsted B.: Spectrum generating operators, and intertwining operators for representations induced from a maximal parabolic subgroups.J. Funct. Anal. 135 (1996), 163–205. MR 1367629
Reference: [6] Hong D.: Eigenvalues of Dirac and Rarita-Schwinger operators.Clifford Algebras and their Applications in Mathematical Physics, Birkhäuser, 2000. Zbl 1080.53044, MR 2025981
Reference: [7] Hong D.: Spectra of higher spin operators.Ph.D. Dissertation, University of Iowa, 2004. MR 2706219
Reference: [8] Kosmann Y.: Dérivées de Lie des spineurs.Ann. Mat. Pura Appl. 91 (1972), 317–395. Zbl 0231.53065, MR 0312413
Reference: [9] Ørsted B.: Conformally invariant differential equations and projective geometry.J. Funct. Anal. 44 (1981), 1–23. Zbl 0507.58048, MR 0638292


Files Size Format View
ArchMathRetro_042-2006-5_6.pdf 267.9Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo