# Article

 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: http://hdl.handle.net/10338.dmlcz/108025 . 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 .

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