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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.
MSC:
 53C28 Twistor methods in differential geometry 22E46 Semisimple Lie groups and their representations
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