Spectrum generating on twistor bundle

Thomas Branson and Doojin Hong


Address.
Thomas Branson, Department of Mathematics, University of Iowa, Iowa City IA 52242, USA
Doojin Hong, Department of Mathematical Sciences, Seoul National University, Seoul Korea

E-mail.
branson@math.uiowa.edu
doojin@math.snu.ac.kr

Abstract.
Spectrum generating technique introduced by \'Olafsson, {\O}rsted, and one of the authors in the paper [BOO:96] 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.