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Spectrum generating on twistor bundle. (English) Zbl 1164.53358
Summary: The spectrum generating technique introduced by T. Branson, G. Ólafsson and B. Ørsted [J. Funct. Anal. 135, 163–205 (1996; Zbl 0841.22011)] 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. Making use of the spectrum generating technique, we give (with some additional calculation) explicit formulas for these intertwinors of all orders.
53C28 Twistor methods in differential geometry
22E46 Semisimple Lie groups and their representations
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