# Article

Full entry | PDF   (0.2 MB)
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.
References:
[1] Branson T.: Group representations arising from Lorentz conformal geometry. J. Funct. Anal. 74 (1987), 199–291. MR 0904819 | Zbl 0643.58036
[2] Branson T.: Nonlinear phenomena in the spectral theory of geometric linear differential operators. Proc. Symp. Pure Math. 59 (1996), 27–65. MR 1392983 | Zbl 0857.58042
[3] Branson T.: Stein-Weiss operators and ellipticity. J. Funct. Anal. 151 (1997), 334–383. MR 1491546 | Zbl 0904.58054
[4] Branson T.: Spectra of self-gradients on spheres. J. Lie Theory 9 (1999), 491–506. MR 1718236 | Zbl 1012.22026
[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
[6] Hong D.: Eigenvalues of Dirac and Rarita-Schwinger operators. Clifford Algebras and their Applications in Mathematical Physics, Birkhäuser, 2000. MR 2025981 | Zbl 1080.53044
[7] Hong D.: Spectra of higher spin operators. Ph.D. Dissertation, University of Iowa, 2004. MR 2706219
[8] Kosmann Y.: Dérivées de Lie des spineurs. Ann. Mat. Pura Appl. 91 (1972), 317–395. MR 0312413 | Zbl 0231.53065
[9] Ørsted B.: Conformally invariant differential equations and projective geometry. J. Funct. Anal. 44 (1981), 1–23. MR 0638292 | Zbl 0507.58048

Partner of