## 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.